Hu, Dongdong; Kong, Linghua; Cai, Wenjun; Wang, Yushun Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions. (English) Zbl 07824756 Numer. Algorithms 95, No. 4, 1953-1980 (2024). MSC: 65-XX 65M06 65M12 65T50 35R11 PDFBibTeX XMLCite \textit{D. Hu} et al., Numer. Algorithms 95, No. 4, 1953--1980 (2024; Zbl 07824756) Full Text: DOI
Wang, Shuaikang; Jiang, Yunzhi; Ge, Yongbin High-order compact difference methods for solving two-dimensional nonlinear wave equations. (English) Zbl 07804281 Electron. Res. Arch. 31, No. 6, 3145-3168 (2023). MSC: 65M06 65N06 65M12 65M15 41A21 35Q53 PDFBibTeX XMLCite \textit{S. Wang} et al., Electron. Res. Arch. 31, No. 6, 3145--3168 (2023; Zbl 07804281) Full Text: DOI
Arora, S.; Bala, I. Numerical study of sine-Gordon equations using Bessel collocation method. (English) Zbl 07780471 Iran. J. Numer. Anal. Optim. 13, No. 4, 728-746 (2023). MSC: 65M70 35L10 PDFBibTeX XMLCite \textit{S. Arora} and \textit{I. Bala}, Iran. J. Numer. Anal. Optim. 13, No. 4, 728--746 (2023; Zbl 07780471) Full Text: DOI
Li, Jin; Qu, Jinzheng Barycentric Lagrange interpolation collocation method for solving the sine-Gordon equation. (English) Zbl 1525.65106 Wave Motion 120, Article ID 103159, 23 p. (2023). MSC: 65M70 35Q53 35L05 65D05 PDFBibTeX XMLCite \textit{J. Li} and \textit{J. Qu}, Wave Motion 120, Article ID 103159, 23 p. (2023; Zbl 1525.65106) Full Text: DOI
Kumar, Sudhir; Mittal, R. C.; Jiwari, Ram Retracted article: A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations. (English) Zbl 1524.65662 Int. J. Comput. Math. 100, No. 7, 1580-1600 (2023); retraction note ibid. 100, No. 9, 1955 (2023). MSC: 65M70 65D07 65M12 35Q53 35L70 65L12 65F15 65M06 65N35 PDFBibTeX XMLCite \textit{S. Kumar} et al., Int. J. Comput. Math. 100, No. 7, 1580--1600 (2023; Zbl 1524.65662) Full Text: DOI
Almushaira, Mustafa Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation. (English) Zbl 07701112 Appl. Math. Comput. 451, Article ID 128039, 24 p. (2023). MSC: 65Mxx 35Qxx 65Lxx PDFBibTeX XMLCite \textit{M. Almushaira}, Appl. Math. Comput. 451, Article ID 128039, 24 p. (2023; Zbl 07701112) Full Text: DOI
Deng, Dingwen; Chen, Jingliang; Wang, Qihong Energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon equation and coupled sine-Gordon equations. (English) Zbl 07694959 Numer. Algorithms 93, No. 3, 1045-1081 (2023). MSC: 65-XX PDFBibTeX XMLCite \textit{D. Deng} et al., Numer. Algorithms 93, No. 3, 1045--1081 (2023; Zbl 07694959) Full Text: DOI
Babu, Athira; Asharaf, Noufal Numerical solution of nonlinear sine-Gordon equation using modified cubic B-spline-based differential quadrature method. (English) Zbl 1524.65706 Comput. Methods Differ. Equ. 11, No. 2, 369-386 (2023). MSC: 65N06 65M22 65N22 35L10 65L06 65D07 65D30 65M12 65M06 65M15 35Q53 PDFBibTeX XMLCite \textit{A. Babu} and \textit{N. Asharaf}, Comput. Methods Differ. Equ. 11, No. 2, 369--386 (2023; Zbl 1524.65706) Full Text: DOI
Taherkhani, Shima; Najafi, Khalilsaraye Iraj; Ghayebi, Bakhtiyar A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations. (English) Zbl 1524.35718 Comput. Methods Differ. Equ. 11, No. 2, 357-368 (2023). MSC: 35R11 65M22 65N35 PDFBibTeX XMLCite \textit{S. Taherkhani} et al., Comput. Methods Differ. Equ. 11, No. 2, 357--368 (2023; Zbl 1524.35718) Full Text: DOI
Ma, Tingting; Zheng, Qianqian; Fu, Yayun Optimal error estimation of two fast structure-preserving algorithms for the Riesz fractional sine-Gordon equation. (English) Zbl 1508.65108 Commun. Nonlinear Sci. Numer. Simul. 119, Article ID 107067, 15 p. (2023). MSC: 65M06 65N06 65M12 15B05 35C08 26A33 35R11 35Q53 PDFBibTeX XMLCite \textit{T. Ma} et al., Commun. Nonlinear Sci. Numer. Simul. 119, Article ID 107067, 15 p. (2023; Zbl 1508.65108) Full Text: DOI
Deng, Dingwen; Wang, Qihong A class of weighted energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon-type equations. (English) Zbl 1504.65171 Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106916, 30 p. (2023). MSC: 65M06 65N06 65M12 65M15 35L05 35Q53 PDFBibTeX XMLCite \textit{D. Deng} and \textit{Q. Wang}, Commun. Nonlinear Sci. Numer. Simul. 117, Article ID 106916, 30 p. (2023; Zbl 1504.65171) Full Text: DOI
Nguyen, Lu Trong Khiem; Smyth, Noel Frederick Modulation theory for radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation. (English) Zbl 1505.35322 J. Nonlinear Sci. 33, No. 1, Paper No. 11, 25 p. (2023). MSC: 35Q53 35Q51 35C08 65M60 65M06 65L06 65N30 PDFBibTeX XMLCite \textit{L. T. K. Nguyen} and \textit{N. F. Smyth}, J. Nonlinear Sci. 33, No. 1, Paper No. 11, 25 p. (2023; Zbl 1505.35322) Full Text: DOI
Niknam, Sepideh; Adibi, Hojatollah; Amirfakhrian, Majid A hybrid LRBF-DQ method for solving nonlinear (2 + 1) dimensional initial-boundary value problems. (English) Zbl 07789072 Eng. Anal. Bound. Elem. 145, 59-71 (2022). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{S. Niknam} et al., Eng. Anal. Bound. Elem. 145, 59--71 (2022; Zbl 07789072) Full Text: DOI
Mirzaee, Farshid; Rezaei, Shadi; Samadyar, Nasrin Solution of time-fractional stochastic nonlinear sine-Gordon equation via finite difference and meshfree techniques. (English) Zbl 07780602 Math. Methods Appl. Sci. 45, No. 7, 3426-3438 (2022). MSC: 65M06 65N35 65D12 60H15 60G22 60J65 26A33 35R11 35R60 35Q53 PDFBibTeX XMLCite \textit{F. Mirzaee} et al., Math. Methods Appl. Sci. 45, No. 7, 3426--3438 (2022; Zbl 07780602) Full Text: DOI
Jha, Navnit; Singh, Bhagat Fourth-order compact scheme based on quasi-variable mesh for three-dimensional mildly nonlinear stationary convection-diffusion equations. (English) Zbl 07778272 Numer. Methods Partial Differ. Equations 38, No. 4, 803-829 (2022). MSC: 65N06 65N50 65N12 65N15 65F05 35J60 35J05 35Q53 PDFBibTeX XMLCite \textit{N. Jha} and \textit{B. Singh}, Numer. Methods Partial Differ. Equations 38, No. 4, 803--829 (2022; Zbl 07778272) Full Text: DOI
Ekomasov, Evgenii G.; Nazarov, Vladimir N.; Samsonov, Kirill Yu. Changing the dynamic parameters of localized breather and soliton waves in the sine-Gordon model with extended impurity, external force, and decay in the autoresonance mode. (English) Zbl 1523.35114 Russ. J. Nonlinear Dyn. 18, No. 2, 217-229 (2022). MSC: 35C08 35Q51 65M06 PDFBibTeX XMLCite \textit{E. G. Ekomasov} et al., Russ. J. Nonlinear Dyn. 18, No. 2, 217--229 (2022; Zbl 1523.35114) Full Text: DOI MNR
Shiralizadeh, Mansour; Alipanah, Amjad; Mohammadi, Maryam Numerical solution of one-dimensional sine-Gordon equation using rational radial basis functions. (English) Zbl 1524.65686 J. Math. Model. 10, No. 3, 387-405 (2022). MSC: 65M70 65N35 65D12 35Q53 65M06 PDFBibTeX XMLCite \textit{M. Shiralizadeh} et al., J. Math. Model. 10, No. 3, 387--405 (2022; Zbl 1524.65686) Full Text: DOI
Hoitmetov, Umid Azadovich Integration of the sine-Gordon equation with a source and an additional term. (English) Zbl 07633028 Rep. Math. Phys. 90, No. 2, 221-240 (2022). MSC: 35-XX 65-XX PDFBibTeX XMLCite \textit{U. A. Hoitmetov}, Rep. Math. Phys. 90, No. 2, 221--240 (2022; Zbl 07633028) Full Text: DOI
Singh, Suruchi; Singh, Swarn; Aggarwal, Anu Cubic B-spline method for non-linear sine-Gordon equation. (English) Zbl 1513.65425 Comput. Appl. Math. 41, No. 8, Paper No. 382, 20 p. (2022). MSC: 65M70 65M06 65N35 65D07 65M12 35Q53 PDFBibTeX XMLCite \textit{S. Singh} et al., Comput. Appl. Math. 41, No. 8, Paper No. 382, 20 p. (2022; Zbl 1513.65425) Full Text: DOI
Arora, Geeta; Joshi, Varun; Mittal, R. C. A spline-based differential quadrature approach to solve sine-Gordon equation in one and two dimension. (English) Zbl 07613768 Fractals 30, No. 7, Article ID 2250153, 14 p. (2022). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{G. Arora} et al., Fractals 30, No. 7, Article ID 2250153, 14 p. (2022; Zbl 07613768) Full Text: DOI
Li, Shanshan; Duan, Yong; Bai, Libing On the meshless quasi-interpolation methods for solving 2D sine-Gordon equations. (English) Zbl 1513.65016 Comput. Appl. Math. 41, No. 8, Paper No. 348, 21 p. (2022). MSC: 65D05 65D12 65D15 65F10 65M12 PDFBibTeX XMLCite \textit{S. Li} et al., Comput. Appl. Math. 41, No. 8, Paper No. 348, 21 p. (2022; Zbl 1513.65016) Full Text: DOI
Yue, Xiaopeng; Fu, Yayun Efficiency energy-preserving cosine pseudo-spectral algorithms for the sine-Gordon equation with Neumann boundary conditions. (English) Zbl 1513.65428 Int. J. Comput. Math. 99, No. 12, 2367-2381 (2022). MSC: 65M70 65L05 PDFBibTeX XMLCite \textit{X. Yue} and \textit{Y. Fu}, Int. J. Comput. Math. 99, No. 12, 2367--2381 (2022; Zbl 1513.65428) Full Text: DOI
Zheng, Hang; Xia, Yonghui; Pinto, Manuel Chaotic motion and control of the driven-damped double sine-Gordon equation. (English) Zbl 1505.34065 Discrete Contin. Dyn. Syst., Ser. B 27, No. 12, 7151-7167 (2022). MSC: 34C28 34C37 34H10 65P20 35L10 35C07 37J40 PDFBibTeX XMLCite \textit{H. Zheng} et al., Discrete Contin. Dyn. Syst., Ser. B 27, No. 12, 7151--7167 (2022; Zbl 1505.34065) Full Text: DOI
Partohaghighi, Mohammad; Inc, Mustafa; Yusuf, Abdullahi; Sulaiman, Tukur A.; Bayram, Mustafa Numerical approximations and conservation laws for the sine-Gordon equation. (English) Zbl 1490.65233 J. Geom. Phys. 178, Article ID 104556, 11 p. (2022). MSC: 65M99 35L65 PDFBibTeX XMLCite \textit{M. Partohaghighi} et al., J. Geom. Phys. 178, Article ID 104556, 11 p. (2022; Zbl 1490.65233) Full Text: DOI
Shi, Wei; Liu, Kai A dissipation-preserving integrator for damped oscillatory Hamiltonian systems. (English) Zbl 1499.65294 J. Comput. Math. 40, No. 4, 573-591 (2022). MSC: 65L05 65L07 65L20 65P10 PDFBibTeX XMLCite \textit{W. Shi} and \textit{K. Liu}, J. Comput. Math. 40, No. 4, 573--591 (2022; Zbl 1499.65294) Full Text: DOI
Deresse, Alemayehu Tamirie Double Sumudu transform iterative method for one-dimensional nonlinear coupled sine-Gordon equation. (English) Zbl 1489.65152 Adv. Math. Phys. 2022, Article ID 6977692, 15 p. (2022). MSC: 65M99 65J15 44A10 35Q53 PDFBibTeX XMLCite \textit{A. T. Deresse}, Adv. Math. Phys. 2022, Article ID 6977692, 15 p. (2022; Zbl 1489.65152) Full Text: DOI
Wang, Yibo; Du, Rui; Chai, Zhenhua Lattice Boltzmann model for time-fractional nonlinear wave equations. (English) Zbl 1499.65591 Adv. Appl. Math. Mech. 14, No. 4, 914-935 (2022). MSC: 65M75 82C40 35Q20 26A33 35R11 PDFBibTeX XMLCite \textit{Y. Wang} et al., Adv. Appl. Math. Mech. 14, No. 4, 914--935 (2022; Zbl 1499.65591) Full Text: DOI
Deng, Dingwen; Wu, Qiang The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations. (English) Zbl 07496461 Numer. Algorithms 89, No. 4, 1663-1693 (2022). MSC: 65Mxx PDFBibTeX XMLCite \textit{D. Deng} and \textit{Q. Wu}, Numer. Algorithms 89, No. 4, 1663--1693 (2022; Zbl 07496461) Full Text: DOI
Mirzaee, Farshid; Rezaei, Shadi; Samadyar, Nasrin Application of combination schemes based on radial basis functions and finite difference to solve stochastic coupled nonlinear time fractional sine-Gordon equations. (English) Zbl 1499.35744 Comput. Appl. Math. 41, No. 1, Paper No. 10, 16 p. (2022). MSC: 35R60 60H15 26A33 65M06 PDFBibTeX XMLCite \textit{F. Mirzaee} et al., Comput. Appl. Math. 41, No. 1, Paper No. 10, 16 p. (2022; Zbl 1499.35744) Full Text: DOI
Jiwari, Ram Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional sine-Gordon equation. (English) Zbl 07776054 Numer. Methods Partial Differ. Equations 37, No. 3, 1965-1992 (2021). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{R. Jiwari}, Numer. Methods Partial Differ. Equations 37, No. 3, 1965--1992 (2021; Zbl 07776054) Full Text: DOI
Cheng, Xinyu; Li, Dong; Quan, Chaoyu; Yang, Wen On a parabolic sine-Gordon model. (English) Zbl 1499.65379 Numer. Math., Theory Methods Appl. 14, No. 4, 1068-1084 (2021). MSC: 65M06 65M12 65M20 65L06 PDFBibTeX XMLCite \textit{X. Cheng} et al., Numer. Math., Theory Methods Appl. 14, No. 4, 1068--1084 (2021; Zbl 1499.65379) Full Text: DOI arXiv
Macías-Díaz, J. E. Nonlinear wave transmission in harmonically driven Hamiltonian sine-Gordon regimes with memory effects. (English) Zbl 1496.65122 Chaos Solitons Fractals 142, Article ID 110362, 12 p. (2021). MSC: 65M06 35L10 PDFBibTeX XMLCite \textit{J. E. Macías-Díaz}, Chaos Solitons Fractals 142, Article ID 110362, 12 p. (2021; Zbl 1496.65122) Full Text: DOI
Singh, Brajesh Kumar; Gupta, Mukesh A new efficient fourth order collocation scheme for solving sine-Gordon equation. (English) Zbl 07490149 Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 138, 18 p. (2021). MSC: 65Mxx 34-XX PDFBibTeX XMLCite \textit{B. K. Singh} and \textit{M. Gupta}, Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 138, 18 p. (2021; Zbl 07490149) Full Text: DOI
Schurz, Henri; Talafha, Abdallah M. Existence, uniqueness, and energy of approximate Fourier solutions of modified stochastic sine-Gordon equation with power-law nonlinearity in 1D. (English) Zbl 1499.35382 Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 126, 22 p. (2021). MSC: 35L20 35R60 60H10 60H15 60H35 65C30 70K20 74J30 PDFBibTeX XMLCite \textit{H. Schurz} and \textit{A. M. Talafha}, Int. J. Appl. Comput. Math. 7, No. 4, Paper No. 126, 22 p. (2021; Zbl 1499.35382) Full Text: DOI
Shokri, Ali; Bahmani, Erfan A study of nonlinear systems arising in the physics of liquid crystals, using MLPG and DMLPG methods. (English) Zbl 07428958 Math. Comput. Simul. 187, 261-281 (2021). MSC: 65-XX 41-XX PDFBibTeX XMLCite \textit{A. Shokri} and \textit{E. Bahmani}, Math. Comput. Simul. 187, 261--281 (2021; Zbl 07428958) Full Text: DOI
Xing, Zhiyong; Wen, Liping A linearized difference scheme for time-fractional sine-Gordon equation. (English) Zbl 1488.35584 Adv. Appl. Math. Mech. 13, No. 2, 285-295 (2021). MSC: 35R11 65M06 65M12 PDFBibTeX XMLCite \textit{Z. Xing} and \textit{L. Wen}, Adv. Appl. Math. Mech. 13, No. 2, 285--295 (2021; Zbl 1488.35584) Full Text: DOI
Liu, Kai; Fu, Ting; Shi, Wei A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting. (English) Zbl 1482.65227 Appl. Numer. Math. 170, 242-254 (2021). MSC: 65P10 65L05 PDFBibTeX XMLCite \textit{K. Liu} et al., Appl. Numer. Math. 170, 242--254 (2021; Zbl 1482.65227) Full Text: DOI
Wang, Jun-Ya; Huang, Qiong-Ao A family of effective structure-preserving schemes with second-order accuracy for the undamped sine-Gordon equation. (English) Zbl 1524.65409 Comput. Math. Appl. 90, 38-45 (2021). MSC: 65M06 65M12 65M15 65M60 65M70 35Q53 35J15 PDFBibTeX XMLCite \textit{J.-Y. Wang} and \textit{Q.-A. Huang}, Comput. Math. Appl. 90, 38--45 (2021; Zbl 1524.65409) Full Text: DOI
Xing, Zhiyong; Wen, Liping; Wang, Wansheng An explicit fourth-order energy-preserving difference scheme for the Riesz space-fractional sine-Gordon equations. (English) Zbl 1524.65422 Math. Comput. Simul. 181, 624-641 (2021). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{Z. Xing} et al., Math. Comput. Simul. 181, 624--641 (2021; Zbl 1524.65422) Full Text: DOI
Fu, Yayun; Cai, Wenjun; Wang, Yushun A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach. (English) Zbl 1467.65082 Appl. Numer. Math. 160, 368-385 (2021). Reviewer: Hendrik Ranocha (MÃŒnster) MSC: 65M06 65M12 35R11 35Q53 PDFBibTeX XMLCite \textit{Y. Fu} et al., Appl. Numer. Math. 160, 368--385 (2021; Zbl 1467.65082) Full Text: DOI arXiv
Xing, Zhiyong; Wen, Liping; Xiao, Hanyu A fourth-order conservative difference scheme for the Riesz space-fractional sine-Gordon equations and its fast implementation. (English) Zbl 1459.65161 Appl. Numer. Math. 159, 221-238 (2021). MSC: 65M06 65M12 65H10 65T50 15B05 35R11 35Q53 PDFBibTeX XMLCite \textit{Z. Xing} et al., Appl. Numer. Math. 159, 221--238 (2021; Zbl 1459.65161) Full Text: DOI
Jagtap, Ameya D. On spatio-temporal dynamics of sine-Gordon soliton in nonlinear non-homogeneous media using fully implicit spectral element scheme. (English) Zbl 1455.65133 Appl. Anal. 100, No. 1, 37-60 (2021). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M70 35C08 65M12 58J45 35L70 35L20 35Q51 PDFBibTeX XMLCite \textit{A. D. Jagtap}, Appl. Anal. 100, No. 1, 37--60 (2021; Zbl 1455.65133) Full Text: DOI
Zhao, Zhihui; Li, Hong Numerical analysis of a continuous Galerkin method for damped sine-Gordon equation. (English) Zbl 07777652 Numer. Methods Partial Differ. Equations 36, No. 6, 1369-1388 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{Z. Zhao} and \textit{H. Li}, Numer. Methods Partial Differ. Equations 36, No. 6, 1369--1388 (2020; Zbl 07777652) Full Text: DOI
Emamjomeh, M.; Abbasbandy, S.; Rostamy, D. Quasi interpolation of radial basis functions-pseudospectral method for solving nonlinear Klein-Gordon and sine-Gordon equations. (English) Zbl 1482.65207 Iran. J. Numer. Anal. Optim. 10, No. 1, 81-106 (2020). MSC: 65N22 65L06 65N35 PDFBibTeX XMLCite \textit{M. Emamjomeh} et al., Iran. J. Numer. Anal. Optim. 10, No. 1, 81--106 (2020; Zbl 1482.65207) Full Text: DOI
Khalouta, Ali; Kadem, Abdelouahab A new efficient method for time-fractional sine-Gordon equation with the Caputo and Caputo-Fabrizio operators. (English) Zbl 1475.65158 J. Prime Res. Math. 16, No. 2, 27-43 (2020). MSC: 65M99 35R11 PDFBibTeX XMLCite \textit{A. Khalouta} and \textit{A. Kadem}, J. Prime Res. Math. 16, No. 2, 27--43 (2020; Zbl 1475.65158) Full Text: Link
Mittal, A. K. A stable time-space Jacobi pseudospectral method for two-dimensional sine-Gordon equation. (English) Zbl 07435096 J. Appl. Math. Comput. 63, No. 1-2, 239-264 (2020). MSC: 65-XX 35C07 35C11 35R11 PDFBibTeX XMLCite \textit{A. K. Mittal}, J. Appl. Math. Comput. 63, No. 1--2, 239--264 (2020; Zbl 07435096) Full Text: DOI
Bouchriti, Anass; Pierre, Morgan; Alaa, Nour Eddine Remarks on the asymptotic behavior of scalar auxiliary variable (SAV) schemes for gradient-like flows. (English) Zbl 1468.65135 J. Appl. Anal. Comput. 10, No. 5, 2198-2219 (2020). MSC: 65M60 65M06 35B40 35Q35 35Q53 PDFBibTeX XMLCite \textit{A. Bouchriti} et al., J. Appl. Anal. Comput. 10, No. 5, 2198--2219 (2020; Zbl 1468.65135) Full Text: DOI
Adak, D.; Natarajan, S. Virtual element method for semilinear sine-Gordon equation over polygonal mesh using product approximation technique. (English) Zbl 1510.65276 Math. Comput. Simul. 172, 224-243 (2020). MSC: 65M99 35Q53 PDFBibTeX XMLCite \textit{D. Adak} and \textit{S. Natarajan}, Math. Comput. Simul. 172, 224--243 (2020; Zbl 1510.65276) Full Text: DOI arXiv
Jagtap, Ameya D. Higher order scheme for sine-Gordon equation in nonlinear non-homogeneous media. (English) Zbl 1466.65155 Bressan, Alberto (ed.) et al., Hyperbolic problems: theory, numerics, applications. Proceedings of the 17th international conference, HYP2018, Pennsylvania State University, University Park, PA, USA, June 25–29, 2018. Springfield, MO: American Institute of Mathematical Sciences (AIMS). AIMS Ser. Appl. Math. 10, 465-474 (2020). MSC: 65M70 35Q55 35C08 39A12 33C45 PDFBibTeX XMLCite \textit{A. D. Jagtap}, AIMS Ser. Appl. Math. 10, 465--474 (2020; Zbl 1466.65155)
Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics. (English) Zbl 1464.65151 Eng. Anal. Bound. Elem. 120, 223-237 (2020). MSC: 65M70 35R11 81R20 PDFBibTeX XMLCite \textit{O. Nikan} et al., Eng. Anal. Bound. Elem. 120, 223--237 (2020; Zbl 1464.65151) Full Text: DOI
Martin-Vergara, Francisca; Rus, Francisco; Villatoro, Francisco R. Padé schemes with Richardson extrapolation for the sine-Gordon equation. (English) Zbl 1452.65170 Commun. Nonlinear Sci. Numer. Simul. 85, Article ID 105243, 14 p. (2020). MSC: 65M06 41A21 35C08 35Q51 35Q53 PDFBibTeX XMLCite \textit{F. Martin-Vergara} et al., Commun. Nonlinear Sci. Numer. Simul. 85, Article ID 105243, 14 p. (2020; Zbl 1452.65170) Full Text: DOI
Latifi, Sobhan; Delkhosh, Mehdi Generalized Lagrange Jacobi-Gauss-Lobatto vs Jacobi-Gauss-Lobatto collocation approximations for solving \((2 + 1)\)-dimensional sine-Gordon equations. (English) Zbl 1452.65277 Math. Methods Appl. Sci. 43, No. 4, 2001-2019 (2020). Reviewer: Hendrik Ranocha (Braunschweig) MSC: 65M70 65M06 65M15 41A10 PDFBibTeX XMLCite \textit{S. Latifi} and \textit{M. Delkhosh}, Math. Methods Appl. Sci. 43, No. 4, 2001--2019 (2020; Zbl 1452.65277) Full Text: DOI
Heydari, Mohammad Hossein; Avazzadeh, Zakieh; Yang, Yin; Cattani, Carlo A cardinal method to solve coupled nonlinear variable-order time fractional sine-Gordon equations. (English) Zbl 1449.35437 Comput. Appl. Math. 39, No. 1, Paper No. 2, 21 p. (2020). MSC: 35R11 26A33 65M70 33C47 PDFBibTeX XMLCite \textit{M. H. Heydari} et al., Comput. Appl. Math. 39, No. 1, Paper No. 2, 21 p. (2020; Zbl 1449.35437) Full Text: DOI
Baccouch, Mahboub A posteriori error analysis of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension. (English) Zbl 1428.65025 J. Comput. Appl. Math. 366, Article ID 112432, 20 p. (2020). MSC: 65M12 65M60 65M15 65M50 35Q53 65L06 35C08 PDFBibTeX XMLCite \textit{M. Baccouch}, J. Comput. Appl. Math. 366, Article ID 112432, 20 p. (2020; Zbl 1428.65025) Full Text: DOI
Guo, Shimin; Mei, Liquan; Hou, Yanren; Zhang, Zhengqiang An efficient finite difference/Hermite-Galerkin spectral method for time-fractional coupled sine-Gordon equations on multidimensional unbounded domains and its application in numerical simulations of vector solitons. (English) Zbl 07683935 Comput. Phys. Commun. 237, 110-128 (2019). MSC: 65-XX 37-XX PDFBibTeX XMLCite \textit{S. Guo} et al., Comput. Phys. Commun. 237, 110--128 (2019; Zbl 07683935) Full Text: DOI
Jha, Navnit; Singh, Bhagat Exponential basis and exponential expanding grids third (fourth)-order compact schemes for nonlinear three-dimensional convection-diffusion-reaction equation. (English) Zbl 1485.65114 Adv. Difference Equ. 2019, Paper No. 339, 27 p. (2019). MSC: 65N06 65N12 65F10 35J25 35J65 PDFBibTeX XMLCite \textit{N. Jha} and \textit{B. Singh}, Adv. Difference Equ. 2019, Paper No. 339, 27 p. (2019; Zbl 1485.65114) Full Text: DOI
Huang, Jianguo; Ju, Lili; Wu, Bo A fast compact time integrator method for a family of general order semilinear evolution equations. (English) Zbl 1452.65161 J. Comput. Phys. 393, 313-336 (2019). MSC: 65M06 65L06 35A01 PDFBibTeX XMLCite \textit{J. Huang} et al., J. Comput. Phys. 393, 313--336 (2019; Zbl 1452.65161) Full Text: DOI
Sukuntee, Norapon; Chaturantabut, Saifon Model order reduction for sine-Gordon equation using POD and DEIM. (English) Zbl 1463.65212 Thai J. Math., Spec. Iss.: Annual Meeting in Mathematics 2018, 222-256 (2019). MSC: 65L99 34A45 PDFBibTeX XMLCite \textit{N. Sukuntee} and \textit{S. Chaturantabut}, Thai J. Math., 222--256 (2019; Zbl 1463.65212) Full Text: Link
Martin-Vergara, Francisca; Rus, Francisco; Villatoro, Francisco R. Padé numerical schemes for the sine-Gordon equation. (English) Zbl 1429.65192 Appl. Math. Comput. 358, 232-243 (2019). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{F. Martin-Vergara} et al., Appl. Math. Comput. 358, 232--243 (2019; Zbl 1429.65192) Full Text: DOI
Baccouch, Mahboub Optimal error estimates of the local discontinuous Galerkin method for the two-dimensional sine-Gordon equation on Cartesian grids. (English) Zbl 1427.65214 Int. J. Numer. Anal. Model. 16, No. 3, 436-462 (2019). MSC: 65M12 65M15 65M60 65N12 65N30 35Q51 35L70 PDFBibTeX XMLCite \textit{M. Baccouch}, Int. J. Numer. Anal. Model. 16, No. 3, 436--462 (2019; Zbl 1427.65214) Full Text: Link
Su, LingDe Numerical solution of two-dimensional nonlinear sine-Gordon equation using localized method of approximate particular solutions. (English) Zbl 1464.65110 Eng. Anal. Bound. Elem. 108, 95-107 (2019). MSC: 65M38 35Q53 PDFBibTeX XMLCite \textit{L. Su}, Eng. Anal. Bound. Elem. 108, 95--107 (2019; Zbl 1464.65110) Full Text: DOI
Jiang, Chaolong; Cai, Wenjun; Wang, Yushun A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach. (English) Zbl 1428.65028 J. Sci. Comput. 80, No. 3, 1629-1655 (2019). MSC: 65M12 65M06 35Q53 PDFBibTeX XMLCite \textit{C. Jiang} et al., J. Sci. Comput. 80, No. 3, 1629--1655 (2019; Zbl 1428.65028) Full Text: DOI arXiv
Xu, Xin; Luo, Xiaopeng; Rabitz, Herschel Numerical meshless solution of high-dimensional sine-Gordon equations via Fourier HDMR-HC approximation. (English) Zbl 1433.65245 J. Math. Chem. 57, No. 7, 1683-1699 (2019). MSC: 65M70 35Q53 65M06 PDFBibTeX XMLCite \textit{X. Xu} et al., J. Math. Chem. 57, No. 7, 1683--1699 (2019; Zbl 1433.65245) Full Text: DOI arXiv
Deng, Dingwen Numerical simulation of the coupled sine-Gordon equations via a linearized and decoupled compact ADI method. (English) Zbl 1419.65016 Numer. Funct. Anal. Optim. 40, No. 9, 1053-1079 (2019). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 65M06 65M12 65M15 35Q53 PDFBibTeX XMLCite \textit{D. Deng}, Numer. Funct. Anal. Optim. 40, No. 9, 1053--1079 (2019; Zbl 1419.65016) Full Text: DOI
Lotfi, Mahmoud; Alipanah, Amjad Legendre spectral element method for solving sine-Gordon equation. (English) Zbl 1459.65200 Adv. Difference Equ. 2019, Paper No. 113, 15 p. (2019). MSC: 65M70 35Q53 65M60 65M06 PDFBibTeX XMLCite \textit{M. Lotfi} and \textit{A. Alipanah}, Adv. Difference Equ. 2019, Paper No. 113, 15 p. (2019; Zbl 1459.65200) Full Text: DOI
Duan, Yali; Kong, Linghua; Chen, Xianjin; Guo, Min Lattice Boltzmann model for two-dimensional generalized sine-Gordon equation. (English) Zbl 1453.65378 J. Appl. Anal. Comput. 8, No. 6, 1645-1663 (2018). MSC: 65M99 65Z05 74J30 74S99 PDFBibTeX XMLCite \textit{Y. Duan} et al., J. Appl. Anal. Comput. 8, No. 6, 1645--1663 (2018; Zbl 1453.65378) Full Text: DOI
Jagtap, Ameya D.; Murthy, A. S. Vasudeva Higher order scheme for two-dimensional inhomogeneous sine-Gordon equation with impulsive forcing. (English) Zbl 1508.65141 Commun. Nonlinear Sci. Numer. Simul. 64, 178-197 (2018). MSC: 65M70 65M60 65N35 65N30 65N55 42C10 65M12 65M15 35C08 35Q53 35Q51 PDFBibTeX XMLCite \textit{A. D. Jagtap} and \textit{A. S. V. Murthy}, Commun. Nonlinear Sci. Numer. Simul. 64, 178--197 (2018; Zbl 1508.65141) Full Text: DOI
Liu, Zeting; Lü, Shujuan; Liu, Fawang Fully discrete spectral methods for solving time fractional nonlinear sine-Gordon equation with smooth and non-smooth solutions. (English) Zbl 1427.65292 Appl. Math. Comput. 333, 213-224 (2018). MSC: 65M70 65M12 35R11 PDFBibTeX XMLCite \textit{Z. Liu} et al., Appl. Math. Comput. 333, 213--224 (2018; Zbl 1427.65292) Full Text: DOI
Xing, Zhiyong; Wen, Liping A conservative difference scheme for the Riesz space-fractional sine-Gordon equation. (English) Zbl 1446.65094 Adv. Difference Equ. 2018, Paper No. 238, 22 p. (2018). MSC: 65M12 65M06 35R11 35Q51 PDFBibTeX XMLCite \textit{Z. Xing} and \textit{L. Wen}, Adv. Difference Equ. 2018, Paper No. 238, 22 p. (2018; Zbl 1446.65094) Full Text: DOI
Zhou, Yanjie; Luo, Zhendong A Crank-Nicolson finite difference scheme for the Riesz space fractional-order parabolic-type sine-Gordon equation. (English) Zbl 1446.65086 Adv. Difference Equ. 2018, Paper No. 216, 7 p. (2018). MSC: 65M06 65M12 35Q53 PDFBibTeX XMLCite \textit{Y. Zhou} and \textit{Z. Luo}, Adv. Difference Equ. 2018, Paper No. 216, 7 p. (2018; Zbl 1446.65086) Full Text: DOI
Fang, Zhichao; Li, Hong; Luo, Zhendong; Liu, Yang Mixed finite volume element method and numerical simulation for sine-Gordon equation. (Chinese. English summary) Zbl 1413.65340 Acta Math. Sci., Ser. A, Chin. Ed. 38, No. 2, 395-416 (2018). MSC: 65M08 65M60 65M12 65M15 35Q53 PDFBibTeX XMLCite \textit{Z. Fang} et al., Acta Math. Sci., Ser. A, Chin. Ed. 38, No. 2, 395--416 (2018; Zbl 1413.65340)
Dutykh, Denys; Caputo, Jean-Guy Wave dynamics on networks: method and application to the sine-Gordon equation. (English) Zbl 1393.65010 Appl. Numer. Math. 131, 54-71 (2018). MSC: 65M06 65P10 35Q35 PDFBibTeX XMLCite \textit{D. Dutykh} and \textit{J.-G. Caputo}, Appl. Numer. Math. 131, 54--71 (2018; Zbl 1393.65010) Full Text: DOI arXiv
Baccouch, Mahboub A posteriori local discontinuous Galerkin error estimates for the one-dimensional sine-Gordon equation. (English) Zbl 1390.65094 Int. J. Comput. Math. 95, No. 4, 815-844 (2018). MSC: 65M12 65M15 65M60 65N12 65N30 35Q51 PDFBibTeX XMLCite \textit{M. Baccouch}, Int. J. Comput. Math. 95, No. 4, 815--844 (2018; Zbl 1390.65094) Full Text: DOI
Baccouch, Mahboub Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation in one space dimension. (English) Zbl 1380.65246 J. Comput. Appl. Math. 333, 292-313 (2018). MSC: 65M60 35L70 65M12 65M15 PDFBibTeX XMLCite \textit{M. Baccouch}, J. Comput. Appl. Math. 333, 292--313 (2018; Zbl 1380.65246) Full Text: DOI
Amrein, Mario; Wihler, Thomas P. Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations. (English) Zbl 1384.65082 Numer. Methods Partial Differ. Equations 33, No. 6, 2005-2022 (2017). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N15 35J61 35B25 65N50 PDFBibTeX XMLCite \textit{M. Amrein} and \textit{T. P. Wihler}, Numer. Methods Partial Differ. Equations 33, No. 6, 2005--2022 (2017; Zbl 1384.65082) Full Text: DOI arXiv
Sheng, Huashan A \({{\text{C}}^0}{{\text{P}}_1}\) time stepping method for solving 2D sine-Gordon equations. (Chinese. English summary) Zbl 1399.65216 J. Nanjing Norm. Univ., Nat. Sci. Ed. 40, No. 1, 1-5 (2017). MSC: 65M22 65M60 35Q53 PDFBibTeX XMLCite \textit{H. Sheng}, J. Nanjing Norm. Univ., Nat. Sci. Ed. 40, No. 1, 1--5 (2017; Zbl 1399.65216) Full Text: DOI
Ekomasov, Evgenii G.; Gumerov, Azamat M.; Murtazin, Ramil R. Interaction of sine-Gordon solitons in the model with attracting impurities. (English) Zbl 1386.35032 Math. Methods Appl. Sci. 40, No. 17, 6178-6186 (2017). MSC: 35C08 35Q51 65M06 PDFBibTeX XMLCite \textit{E. G. Ekomasov} et al., Math. Methods Appl. Sci. 40, No. 17, 6178--6186 (2017; Zbl 1386.35032) Full Text: DOI
Shi, Dong-yang; Wang, Fen-ling; Zhao, Yan-min High accuracy analysis of the lowest order \(H^1\)-Galerkin mixed finite element method for nonlinear sine-Gordon equations. (English) Zbl 1372.65312 Acta Math. Appl. Sin., Engl. Ser. 33, No. 3, 699-708 (2017). MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{D.-y. Shi} et al., Acta Math. Appl. Sin., Engl. Ser. 33, No. 3, 699--708 (2017; Zbl 1372.65312) Full Text: DOI
Duan, Yali; Kong, Linghua; Guo, Min Numerical simulation of a class of nonlinear wave equations by lattice Boltzmann method. (English) Zbl 1372.65286 Commun. Math. Stat. 5, No. 1, 13-35 (2017). MSC: 65M75 35L70 35Q40 PDFBibTeX XMLCite \textit{Y. Duan} et al., Commun. Math. Stat. 5, No. 1, 13--35 (2017; Zbl 1372.65286) Full Text: DOI
Vo Anh Khoa; Mai Thanh Nhat Truong; Nguyen Ho Minh Duy; Nguyen Huy Tuan The Cauchy problem of coupled elliptic sine-Gordon equations with noise: analysis of a general kernel-based regularization and reliable tools of computing. (English) Zbl 1368.65217 Comput. Math. Appl. 73, No. 1, 141-162 (2017). MSC: 65N20 65N30 35J57 35L53 35L71 PDFBibTeX XMLCite \textit{Vo Anh Khoa} et al., Comput. Math. Appl. 73, No. 1, 141--162 (2017; Zbl 1368.65217) Full Text: DOI arXiv
Dehghan, Mehdi; Abbaszadeh, Mostafa Two meshless procedures: moving Kriging interpolation and element-free Galerkin for fractional PDEs. (English) Zbl 1369.65121 Appl. Anal. 96, No. 6, 936-969 (2017). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M60 65M12 65M06 35R11 35Q40 35L20 65M15 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Appl. Anal. 96, No. 6, 936--969 (2017; Zbl 1369.65121) Full Text: DOI
Baccouch, Mahboub Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation. (English) Zbl 1367.65139 Int. J. Comput. Math. 94, No. 2, 316-344 (2017). Reviewer: Abdallah Bradji (Annaba) MSC: 65M60 65M12 65M15 35Q51 35Q53 PDFBibTeX XMLCite \textit{M. Baccouch}, Int. J. Comput. Math. 94, No. 2, 316--344 (2017; Zbl 1367.65139) Full Text: DOI
Zadvan, Homa; Rashidinia, Jalil Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term. (English) Zbl 1358.65067 Numer. Algorithms 74, No. 2, 289-306 (2017). MSC: 65M70 35L70 65M12 65M06 PDFBibTeX XMLCite \textit{H. Zadvan} and \textit{J. Rashidinia}, Numer. Algorithms 74, No. 2, 289--306 (2017; Zbl 1358.65067) Full Text: DOI
Baccouch, Mahboub Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation on Cartesian grids. (English) Zbl 1355.65114 Appl. Numer. Math. 113, 124-155 (2017). MSC: 65M12 35L70 35G40 65M60 65M15 65M50 PDFBibTeX XMLCite \textit{M. Baccouch}, Appl. Numer. Math. 113, 124--155 (2017; Zbl 1355.65114) Full Text: DOI
Ekomasov, Evgenii G.; Gumerov, Azamat M.; Kudryavtsev, Roman V. Resonance dynamics of kinks in the sine-Gordon model with impurity, external force and damping. (English) Zbl 1350.35024 J. Comput. Appl. Math. 312, 198-208 (2017). MSC: 35B34 35C08 35Q51 65M06 35L71 PDFBibTeX XMLCite \textit{E. G. Ekomasov} et al., J. Comput. Appl. Math. 312, 198--208 (2017; Zbl 1350.35024) Full Text: DOI
Li, Xiaolin; Zhang, Shougui; Wang, Yan; Chen, Hao Analysis and application of the element-free Galerkin method for nonlinear sine-Gordon and generalized sinh-Gordon equations. (English) Zbl 1443.65211 Comput. Math. Appl. 71, No. 8, 1655-1678 (2016). MSC: 65M60 65M15 35L71 PDFBibTeX XMLCite \textit{X. Li} et al., Comput. Math. Appl. 71, No. 8, 1655--1678 (2016; Zbl 1443.65211) Full Text: DOI
Ran, Maohua; Zhang, Chengjian Compact difference scheme for a class of fractional-in-space nonlinear damped wave equations in two space dimensions. (English) Zbl 1443.65138 Comput. Math. Appl. 71, No. 5, 1151-1162 (2016). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{M. Ran} and \textit{C. Zhang}, Comput. Math. Appl. 71, No. 5, 1151--1162 (2016; Zbl 1443.65138) Full Text: DOI
Tuckwell, Henry C. Numerical solutions of some stochastic hyperbolic wave equations including sine-Gordon equation. (English) Zbl 1467.65097 Wave Motion 65, 130-146 (2016). MSC: 65M75 35L71 35R60 PDFBibTeX XMLCite \textit{H. C. Tuckwell}, Wave Motion 65, 130--146 (2016; Zbl 1467.65097) Full Text: DOI
Chang, Chih-Wen; Liu, Chein-Shan An implicit Lie-group iterative scheme for solving the nonlinear Klein-Gordon and sine-Gordon equations. (English) Zbl 1446.65125 Appl. Math. Modelling 40, No. 2, 1157-1167 (2016). MSC: 65M70 35Q53 65M06 65M12 PDFBibTeX XMLCite \textit{C.-W. Chang} and \textit{C.-S. Liu}, Appl. Math. Modelling 40, No. 2, 1157--1167 (2016; Zbl 1446.65125) Full Text: DOI
Schurz, Henri; Talafha, Abdallah M. Existence, uniqueness, and energy of modified stochastic sine-Gordon equation with multiplicative noise on one-dimensional domain. (English) Zbl 1415.60079 Budzban, Gregory (ed.) et al., Probability on algebraic and geometric structures. International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, Southern Illinois University, Carbondale, IL, USA, June 5–7, 2014. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 668, 179-197 (2016). MSC: 60H15 35R60 37H10 60H10 60H30 65N30 PDFBibTeX XMLCite \textit{H. Schurz} and \textit{A. M. Talafha}, Contemp. Math. 668, 179--197 (2016; Zbl 1415.60079) Full Text: DOI
Akgül, Ali; Inc, Mustafa; Kilicman, Adem; Baleanu, Dumitru A new approach for one-dimensional sine-Gordon equation. (English) Zbl 1422.65274 Adv. Difference Equ. 2016, Paper No. 8, 20 p. (2016). MSC: 65M70 35Q53 65M06 65M12 35Q51 PDFBibTeX XMLCite \textit{A. Akgül} et al., Adv. Difference Equ. 2016, Paper No. 8, 20 p. (2016; Zbl 1422.65274) Full Text: DOI
Jiang, Chaolong; Sun, Jianqiang; Luo, Siyu High order energy-preserving method of the sine-Gordon equation. (Chinese. English summary) Zbl 1363.35319 Numer. Math., Nanjing 38, No. 1, 42-51 (2016). MSC: 35Q53 37K05 65N99 PDFBibTeX XMLCite \textit{C. Jiang} et al., Numer. Math., Nanjing 38, No. 1, 42--51 (2016; Zbl 1363.35319)
Gupta, A. K.; Ray, S. Saha A novel attempt for finding comparatively accurate solution for sine-Gordon equation comprising Riesz space fractional derivative. (English) Zbl 1416.65379 Math. Methods Appl. Sci. 39, No. 11, 2871-2882 (2016). MSC: 65M70 35R11 35L71 65T60 PDFBibTeX XMLCite \textit{A. K. Gupta} and \textit{S. S. Ray}, Math. Methods Appl. Sci. 39, No. 11, 2871--2882 (2016; Zbl 1416.65379) Full Text: DOI
Dehghan, Mehdi; Safarpoor, Mansour The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations. (English) Zbl 1342.65224 Math. Methods Appl. Sci. 39, No. 10, 2461-2476 (2016). MSC: 65N38 35R11 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Safarpoor}, Math. Methods Appl. Sci. 39, No. 10, 2461--2476 (2016; Zbl 1342.65224) Full Text: DOI
Porubov, A. V.; Fradkov, A. L.; Andrievsky, B. R. Feedback control for some solutions of the sine-Gordon equation. (English) Zbl 1410.93055 Appl. Math. Comput. 269, 17-22 (2015). MSC: 93C20 65M20 35L71 65L05 65M06 93B52 PDFBibTeX XMLCite \textit{A. V. Porubov} et al., Appl. Math. Comput. 269, 17--22 (2015; Zbl 1410.93055) Full Text: DOI
Ilati, Mohammad; Dehghan, Mehdi The use of radial basis functions (RBFs) collocation and RBF-QR methods for solving the coupled nonlinear sine-Gordon equations. (English) Zbl 1403.65092 Eng. Anal. Bound. Elem. 52, 99-109 (2015). MSC: 65M70 35Q53 PDFBibTeX XMLCite \textit{M. Ilati} and \textit{M. Dehghan}, Eng. Anal. Bound. Elem. 52, 99--109 (2015; Zbl 1403.65092) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa; Mohebbi, Akbar An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations. (English) Zbl 1403.65082 Eng. Anal. Bound. Elem. 50, 412-434 (2015). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{M. Dehghan} et al., Eng. Anal. Bound. Elem. 50, 412--434 (2015; Zbl 1403.65082) Full Text: DOI
Xu, Xin; Lu, Zhenzhou; Luo, Xiaopeng A numerical meshless method of soliton-like structures model via an optimal sampling density based kernel interpolation. (English) Zbl 1378.65046 Comput. Phys. Commun. 192, 12-22 (2015). MSC: 65D05 35Q51 PDFBibTeX XMLCite \textit{X. Xu} et al., Comput. Phys. Commun. 192, 12--22 (2015; Zbl 1378.65046) Full Text: DOI
Moghaderi, Hamid; Dehghan, Mehdi A multigrid compact finite difference method for solving the one-dimensional nonlinear sine-Gordon equation. (English) Zbl 1335.35219 Math. Methods Appl. Sci. 38, No. 17, 3901-3922 (2015). MSC: 35Q53 65M06 65M55 65F50 PDFBibTeX XMLCite \textit{H. Moghaderi} and \textit{M. Dehghan}, Math. Methods Appl. Sci. 38, No. 17, 3901--3922 (2015; Zbl 1335.35219) Full Text: DOI
Geng, Xiaoyue; Liu, Xiaohua A high accuracy implicit compact difference method for solving the generalized sine-Gordon equations. (Chinese. English summary) Zbl 1340.65169 Math. Numer. Sin. 37, No. 2, 199-212 (2015). MSC: 65M06 35Q40 65M12 PDFBibTeX XMLCite \textit{X. Geng} and \textit{X. Liu}, Math. Numer. Sin. 37, No. 2, 199--212 (2015; Zbl 1340.65169)