Zhang, Jun; Lin, Shimin; Wang, JinRong Stability and convergence analysis of Fourier pseudo-spectral method for FitzHugh-Nagumo model. (English) Zbl 1447.65104 Appl. Numer. Math. 157, 563-578 (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65M70 65M06 65N35 65M12 65M15 35Q53 PDF BibTeX XML Cite \textit{J. Zhang} et al., Appl. Numer. Math. 157, 563--578 (2020; Zbl 1447.65104) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi; Khodadadian, Amirreza; Heitzinger, Clemens Error analysis of interpolating element free Galerkin method to solve non-linear extended Fisher-Kolmogorov equation. (English) Zbl 1446.65103 Comput. Math. Appl. 80, No. 1, 247-262 (2020). MSC: 65M60 65N30 65M06 65M12 65M15 65K10 35Q92 PDF BibTeX XML Cite \textit{M. Abbaszadeh} et al., Comput. Math. Appl. 80, No. 1, 247--262 (2020; Zbl 1446.65103) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving Kriging interpolation shape functions with the weighted essentially non-oscillatory method. (English) Zbl 07263930 Commun. Nonlinear Sci. Numer. Simul. 68, 220-239 (2019). MSC: 65M06 65M60 PDF BibTeX XML Cite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Commun. Nonlinear Sci. Numer. Simul. 68, 220--239 (2019; Zbl 07263930) Full Text: DOI
Doha, E. H.; Hafez, R. M.; Youssri, Y. H. Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations. (English) Zbl 1442.65290 Comput. Math. Appl. 78, No. 3, 889-904 (2019). MSC: 65M70 65M60 35L50 PDF BibTeX XML Cite \textit{E. H. Doha} et al., Comput. Math. Appl. 78, No. 3, 889--904 (2019; Zbl 1442.65290) Full Text: DOI
Zhang, Haixiang; Yang, Xuehua; Xu, Da A high-order numerical method for solving the 2D fourth-order reaction-diffusion equation. (English) Zbl 1412.65122 Numer. Algorithms 80, No. 3, 849-877 (2019). MSC: 65M12 65M06 65M70 35S10 65D07 35R11 65M15 35K57 PDF BibTeX XML Cite \textit{H. Zhang} et al., Numer. Algorithms 80, No. 3, 849--877 (2019; Zbl 1412.65122) Full Text: DOI
Gao, Yali; Mei, Liquan; Li, Rui Galerkin methods for the Davey-Stewartson equations. (English) Zbl 1427.65246 Appl. Math. Comput. 328, 144-161 (2018). MSC: 65M60 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{Y. Gao} et al., Appl. Math. Comput. 328, 144--161 (2018; Zbl 1427.65246) Full Text: DOI
Liang, Xiao; Bhatt, Harish Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation. (English) Zbl 1448.65186 Adv. Difference Equ. 2018, Paper No. 476, 17 p. (2018). MSC: 65M70 65M12 35Q55 PDF BibTeX XML Cite \textit{X. Liang} and \textit{H. Bhatt}, Adv. Difference Equ. 2018, Paper No. 476, 17 p. (2018; Zbl 1448.65186) Full Text: DOI
Thirumalai, Sagithya; Seshadri, Rajeswari Spectral analysis on Burgers’ equation and its solutions using three different basis functions. (English) Zbl 1407.65227 Int. J. Appl. Comput. Math. 4, No. 3, Paper No. 93, 21 p. (2018). MSC: 65M70 35Q35 35Q53 65L06 35K55 76L05 41A10 41A50 42C10 33C45 PDF BibTeX XML Cite \textit{S. Thirumalai} and \textit{R. Seshadri}, Int. J. Appl. Comput. Math. 4, No. 3, Paper No. 93, 21 p. (2018; Zbl 1407.65227) Full Text: DOI
Alrehaili, Dina Abdullah; Al-Maturi, Dalal Adnan; Al-Aidarous, Eman Salem; Ahmad, Fayyaz An eighth order frozen Jacobian iterative method for solving nonlinear IVPs and BVPs. (English) Zbl 1427.65072 J. Math. Comput. Sci., JMCS 17, No. 3, 378-399 (2017). MSC: 65H10 PDF BibTeX XML Cite \textit{D. A. Alrehaili} et al., J. Math. Comput. Sci., JMCS 17, No. 3, 378--399 (2017; Zbl 1427.65072) Full Text: DOI
Albuohimad, Basim; Adibi, Hojatollah On a hybrid spectral exponential Chebyshev method for time-fractional coupled Burgers equations on a semi-infinite domain. (English) Zbl 1422.65275 Adv. Difference Equ. 2017, Paper No. 85, 18 p. (2017). MSC: 65M70 35R11 65M12 PDF BibTeX XML Cite \textit{B. Albuohimad} and \textit{H. Adibi}, Adv. Difference Equ. 2017, Paper No. 85, 18 p. (2017; Zbl 1422.65275) Full Text: DOI
Lee, Hyun Geun A semi-analytical Fourier spectral method for the Swift-Hohenberg equation. (English) Zbl 1397.65205 Comput. Math. Appl. 74, No. 8, 1885-1896 (2017). MSC: 65M70 65M12 35Q35 35C05 PDF BibTeX XML Cite \textit{H. G. Lee}, Comput. Math. Appl. 74, No. 8, 1885--1896 (2017; Zbl 1397.65205) Full Text: DOI
Parand, Kourosh; Mazaheri, Pooria; Delkhosh, Mehdi; Ghaderi, Amin New numerical solutions for solving Kidder equation by using the rational Jacobi functions. (English) Zbl 1380.34038 S\(\vec{\text{e}}\)MA J. 74, No. 4, 569-583 (2017). MSC: 34A45 34B15 34B40 65L60 PDF BibTeX XML Cite \textit{K. Parand} et al., S\(\vec{\text{e}}\)MA J. 74, No. 4, 569--583 (2017; Zbl 1380.34038) Full Text: DOI
Ahmad, Fayyaz; Rehman, Shafiq Ur; Ullah, Malik Zaka; Aljahdali, Hani Moaiteq; Ahmad, Shahid; Alshomrani, Ali Saleh; Carrasco, Juan A.; Ahmad, Shamshad; Sivasankaran, Sivanandam Frozen Jacobian multistep iterative method for solving nonlinear IVPs and BVPs. (English) Zbl 1367.65077 Complexity 2017, Article ID 9407656, 30 p. (2017). MSC: 65H10 65M70 PDF BibTeX XML Cite \textit{F. Ahmad} et al., Complexity 2017, Article ID 9407656, 30 p. (2017; Zbl 1367.65077) Full Text: DOI
Qasim, Sabahat; Ali, Zulifqar; Ahmad, Fayyaz; Serra-Capizzano, S.; Ullah, Malik Zaka; Mahmood, Arshad Solving systems of nonlinear equations when the nonlinearity is expensive. (English) Zbl 1443.65074 Comput. Math. Appl. 71, No. 7, 1464-1478 (2016). MSC: 65H10 PDF BibTeX XML Cite \textit{S. Qasim} et al., Comput. Math. Appl. 71, No. 7, 1464--1478 (2016; Zbl 1443.65074) Full Text: DOI
Qasim, Uswah; Ali, Zulifqar; Ahmad, Fayyaz; Serra-Capizzano, Stefano; Zaka Ullah, Malik; Asma, Mir Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method. (English) Zbl 07042327 Algorithms (Basel) 9, No. 1, Paper No. 18, 17 p. (2016). MSC: 65 93 PDF BibTeX XML Cite \textit{U. Qasim} et al., Algorithms (Basel) 9, No. 1, Paper No. 18, 17 p. (2016; Zbl 07042327) Full Text: DOI
Seadawy, A. R.; El-Kalaawy, O. H.; Aldenari, R. B. Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability. (English) Zbl 1410.35022 Appl. Math. Comput. 280, 57-71 (2016). MSC: 35C08 35Q53 76D33 PDF BibTeX XML Cite \textit{A. R. Seadawy} et al., Appl. Math. Comput. 280, 57--71 (2016; Zbl 1410.35022) 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 PDF BibTeX XML Cite \textit{A. Akgül} et al., Adv. Difference Equ. 2016, Paper No. 8, 20 p. (2016; Zbl 1422.65274) Full Text: DOI
Bhrawy, A. H.; Abdelkawy, M. A. Efficient spectral collocation algorithm for solving parabolic inverse problems. (English) Zbl 1359.65176 Int. J. Comput. Methods 13, No. 6, Article ID 1650036, 22 p. (2016). MSC: 65M32 65M70 PDF BibTeX XML Cite \textit{A. H. Bhrawy} and \textit{M. A. Abdelkawy}, Int. J. Comput. Methods 13, No. 6, Article ID 1650036, 22 p. (2016; Zbl 1359.65176) Full Text: DOI
Ekomasov, E. G.; Salimov, R. K. Pseudo-spectral Fourier method as applied to finding localized spherical soliton solutions of \((3 + 1)\)-dimensional Klein-Gordon equations. (English. Russian original) Zbl 1362.35077 Comput. Math. Math. Phys. 56, No. 9, 1604-1610 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 9, 1628-1634 (2016). MSC: 35C08 35L71 PDF BibTeX XML Cite \textit{E. G. Ekomasov} and \textit{R. K. Salimov}, Comput. Math. Math. Phys. 56, No. 9, 1604--1610 (2016; Zbl 1362.35077); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 9, 1628--1634 (2016) Full Text: DOI
Mehrpouya, Mohammad Ali An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics. (English) Zbl 1343.65086 Math. Methods Appl. Sci. 39, No. 12, 3204-3214 (2016). MSC: 65L05 34B16 65M70 34K28 85-08 PDF BibTeX XML Cite \textit{M. A. Mehrpouya}, Math. Methods Appl. Sci. 39, No. 12, 3204--3214 (2016; Zbl 1343.65086) Full Text: DOI
Ahmad, Fayyaz; Tohidi, Emran; Carrasco, Juan A. A parameterized multi-step Newton method for solving systems of nonlinear equations. (English) Zbl 1350.65046 Numer. Algorithms 71, No. 3, 631-653 (2016). Reviewer: Przemysław Stpiczyński (Lublin) MSC: 65H10 65N22 PDF BibTeX XML Cite \textit{F. Ahmad} et al., Numer. Algorithms 71, No. 3, 631--653 (2016; Zbl 1350.65046) Full Text: DOI
He, Dongdong; Pan, Kejia A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation. (English) Zbl 1410.65312 Appl. Math. Comput. 271, 323-336 (2015). MSC: 65M06 35Q53 65M12 PDF BibTeX XML Cite \textit{D. He} and \textit{K. Pan}, Appl. Math. Comput. 271, 323--336 (2015; Zbl 1410.65312) Full Text: DOI arXiv
Yuksel, Gamze; Isik, Osman Rasit; Sezer, Mehmet Error analysis of the Chebyshev collocation method for linear second-order partial differential equations. (English) Zbl 1325.65141 Int. J. Comput. Math. 92, No. 10, 2121-2138 (2015). MSC: 65M70 35G05 PDF BibTeX XML Cite \textit{G. Yuksel} et al., Int. J. Comput. Math. 92, No. 10, 2121--2138 (2015; Zbl 1325.65141) Full Text: DOI
Liu, Chunxiao; Zhu, Shengfeng Laguerre pseudospectral approximation to the Thomas-Fermi equation. (English) Zbl 1316.34026 J. Comput. Appl. Math. 282, 251-261 (2015). Reviewer: Ekin Uğurlu (Ankara) MSC: 34B16 34B40 34A45 PDF BibTeX XML Cite \textit{C. Liu} and \textit{S. Zhu}, J. Comput. Appl. Math. 282, 251--261 (2015; Zbl 1316.34026) Full Text: DOI
Bhrawy, A. H.; Alghamdi, M. A.; Alaidarous, Eman S. An efficient numerical approach for solving nonlinear coupled hyperbolic partial differential equations with nonlocal conditions. (English) Zbl 1449.65241 Abstr. Appl. Anal. 2014, Article ID 295936, 14 p. (2014). MSC: 65M60 65N35 65L06 65M32 35R05 35C08 35L70 PDF BibTeX XML Cite \textit{A. H. Bhrawy} et al., Abstr. Appl. Anal. 2014, Article ID 295936, 14 p. (2014; Zbl 1449.65241) Full Text: DOI
Tatari, Mehdi; Haghighi, Mahboobeh A generalized Laguerre-Legendre spectral collocation method for solving initial-boundary value problems. (English) Zbl 1427.65304 Appl. Math. Modelling 38, No. 4, 1351-1364 (2014). MSC: 65M70 PDF BibTeX XML Cite \textit{M. Tatari} and \textit{M. Haghighi}, Appl. Math. Modelling 38, No. 4, 1351--1364 (2014; Zbl 1427.65304) Full Text: DOI
Helal, M. A.; Seadawy, A. R.; Zekry, M. H. Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation. (English) Zbl 1410.35169 Appl. Math. Comput. 232, 1094-1103 (2014). MSC: 35Q53 35Q35 PDF BibTeX XML Cite \textit{M. A. Helal} et al., Appl. Math. Comput. 232, 1094--1103 (2014; Zbl 1410.35169) Full Text: DOI
Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; Van Gorder, Robert A. Jacobi-Gauss-Lobatto collocation method for the numerical solution of \(1+1\) nonlinear Schrödinger equations. (English) Zbl 1349.65511 J. Comput. Phys. 261, 244-255 (2014). MSC: 65M70 35Q55 PDF BibTeX XML Cite \textit{E. H. Doha} et al., J. Comput. Phys. 261, 244--255 (2014; Zbl 1349.65511) Full Text: DOI
Taleei, Ameneh; Dehghan, Mehdi Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations. (English) Zbl 1348.35246 Comput. Phys. Commun. 185, No. 6, 1515-1528 (2014). MSC: 35Q55 35C08 65M70 65M55 PDF BibTeX XML Cite \textit{A. Taleei} and \textit{M. Dehghan}, Comput. Phys. Commun. 185, No. 6, 1515--1528 (2014; Zbl 1348.35246) Full Text: DOI
Bhrawy, A. H. An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system. (English) Zbl 1339.65188 Appl. Math. Comput. 247, 30-46 (2014). MSC: 65M70 35L70 35Q55 PDF BibTeX XML Cite \textit{A. H. Bhrawy}, Appl. Math. Comput. 247, 30--46 (2014; Zbl 1339.65188) Full Text: DOI
Rashid, Abdur; Abbas, Muhammad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd Numerical solution of the coupled viscous Burgers equations by Chebyshev-Legendre pseudo-spectral method. (English) Zbl 1336.65177 Appl. Math. Comput. 245, 372-381 (2014). MSC: 65M70 PDF BibTeX XML Cite \textit{A. Rashid} et al., Appl. Math. Comput. 245, 372--381 (2014; Zbl 1336.65177) Full Text: DOI
Eslahchi, M. R.; Dehghan, Mehdi; Parvizi, M. Application of the collocation method for solving nonlinear fractional integro-differential equations. (English) Zbl 1296.65106 J. Comput. Appl. Math. 257, 105-128 (2014). MSC: 65L60 33C45 44A45 46C99 34A08 PDF BibTeX XML Cite \textit{M. R. Eslahchi} et al., J. Comput. Appl. Math. 257, 105--128 (2014; Zbl 1296.65106) Full Text: DOI
Dehghan, Mehdi; Saray, Behzad Nemati; Lakestani, Mehrdad Mixed finite difference and Galerkin methods for solving Burgers equations using interpolating scaling functions. (English) Zbl 1417.37271 Math. Methods Appl. Sci. 37, No. 6, 894-912 (2014). MSC: 37L65 65N06 65N22 65N30 PDF BibTeX XML Cite \textit{M. Dehghan} et al., Math. Methods Appl. Sci. 37, No. 6, 894--912 (2014; Zbl 1417.37271) Full Text: DOI
Fakhar-Izadi, Farhad; Dehghan, Mehdi An efficient pseudo-spectral Legendre-Galerkin method for solving a nonlinear partial integro-differential equation arising in population dynamics. (English) Zbl 1279.65143 Math. Methods Appl. Sci. 36, No. 12, 1485-1511 (2013). MSC: 65R20 45K05 45G10 PDF BibTeX XML Cite \textit{F. Fakhar-Izadi} and \textit{M. Dehghan}, Math. Methods Appl. Sci. 36, No. 12, 1485--1511 (2013; Zbl 1279.65143) Full Text: DOI
Soori, Zoleikha; Aminataei, Azim The spectral method for solving sine-Gordon equation using a new orthogonal polynomial. (English) Zbl 1264.65169 ISRN Appl. Math. 2012, Article ID 462731, 12 p. (2012). MSC: 65M70 35L71 35L20 PDF BibTeX XML Cite \textit{Z. Soori} and \textit{A. Aminataei}, ISRN Appl. Math. 2012, Article ID 462731, 12 p. (2012; Zbl 1264.65169) Full Text: DOI
Salehi, Rezvan; Dehghan, Mehdi The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic Hamilton-Jacobi equations. (English) Zbl 1238.65100 Comput. Math. Appl. 63, No. 3, 629-644 (2012). MSC: 65M70 PDF BibTeX XML Cite \textit{R. Salehi} and \textit{M. Dehghan}, Comput. Math. Appl. 63, No. 3, 629--644 (2012; Zbl 1238.65100) Full Text: DOI
Lakestani, Mehrdad; Dehghan, Mehdi Numerical solutions of the generalized kuramoto-sivashinsky equation using B-spline functions. (English) Zbl 1236.65114 Appl. Math. Modelling 36, No. 2, 605-617 (2012). MSC: 65M06 PDF BibTeX XML Cite \textit{M. Lakestani} and \textit{M. Dehghan}, Appl. Math. Modelling 36, No. 2, 605--617 (2012; Zbl 1236.65114) Full Text: DOI