Ku Sahoo, Sanjay; Gupta, Vikas; Dubey, Shruti A robust higher-order finite difference technique for a time-fractional singularly perturbed problem. (English) Zbl 07764057 Math. Comput. Simul. 215, 43-68 (2024). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{S. Ku Sahoo} et al., Math. Comput. Simul. 215, 43--68 (2024; Zbl 07764057) Full Text: DOI
Qiu, Wenlin; Xiao, Xu; Li, Kexin Second-order accurate numerical scheme with graded meshes for the nonlinear partial integrodifferential equation arising from viscoelasticity. (English) Zbl 1524.65978 Commun. Nonlinear Sci. Numer. Simul. 116, Article ID 106804, 19 p. (2023). MSC: 65R20 45K05 35R11 65M12 65M22 65M60 PDFBibTeX XMLCite \textit{W. Qiu} et al., Commun. Nonlinear Sci. Numer. Simul. 116, Article ID 106804, 19 p. (2023; Zbl 1524.65978) Full Text: DOI arXiv
Li, Xiaoli; Rui, Hongxing Superconvergence of MAC scheme for a coupled free flow-porous media system with heat transport on non-uniform grids. (English) Zbl 1486.65115 J. Sci. Comput. 90, No. 3, Paper No. 90, 32 p. (2022). MSC: 65M06 65M12 65M15 76D07 76S05 80A19 35Q35 PDFBibTeX XMLCite \textit{X. Li} and \textit{H. Rui}, J. Sci. Comput. 90, No. 3, Paper No. 90, 32 p. (2022; Zbl 1486.65115) Full Text: DOI
Qiao, Leijie; Tang, Bo An accurate, robust, and efficient finite difference scheme with graded meshes for the time-fractional Burgers’ equation. (English) Zbl 1524.35709 Appl. Math. Lett. 128, Article ID 107908, 7 p. (2022). MSC: 35R11 65M06 35Q53 65M12 65M15 PDFBibTeX XMLCite \textit{L. Qiao} and \textit{B. Tang}, Appl. Math. Lett. 128, Article ID 107908, 7 p. (2022; Zbl 1524.35709) Full Text: DOI
Qiao, Haili; Cheng, Aijie Finite difference method on non-uniform meshes for time fractional diffusion problem. (English) Zbl 1476.65187 Comput. Methods Appl. Math. 21, No. 4, 899-911 (2021). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{H. Qiao} and \textit{A. Cheng}, Comput. Methods Appl. Math. 21, No. 4, 899--911 (2021; Zbl 1476.65187) Full Text: DOI
Qiao, Leijie; Qiu, Wenlin; Xu, Da A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem. (English) Zbl 1524.65386 Comput. Math. Appl. 102, 137-145 (2021). MSC: 65M06 35K57 35R11 45K05 65M12 65M22 65M50 65R20 PDFBibTeX XMLCite \textit{L. Qiao} et al., Comput. Math. Appl. 102, 137--145 (2021; Zbl 1524.65386) Full Text: DOI
Bai, Xixian; Rui, Hongxing New energy analysis of Yee scheme for metamaterial Maxwell’s equations on non-uniform rectangular meshes. (English) Zbl 1488.65221 Adv. Appl. Math. Mech. 13, No. 6, 1355-1383 (2021). MSC: 65M06 65M12 35L15 78A48 35Q60 35B35 78M20 PDFBibTeX XMLCite \textit{X. Bai} and \textit{H. Rui}, Adv. Appl. Math. Mech. 13, No. 6, 1355--1383 (2021; Zbl 1488.65221) Full Text: DOI
Hieu, L. M.; Thanh, D. N. H.; Tu, T. T. Second order monotone finite-difference schemes on non-uniform grids for multi-dimensional convection-diffusion problem with a boundary condition of the third kind. (English) Zbl 1496.65113 Lobachevskii J. Math. 42, No. 7, 1661-1674 (2021). MSC: 65M06 65N06 76R50 35B65 35B45 PDFBibTeX XMLCite \textit{L. M. Hieu} et al., Lobachevskii J. Math. 42, No. 7, 1661--1674 (2021; Zbl 1496.65113) Full Text: DOI
Zlotnik, Alexander; Čiegis, Raimondas A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes. (English) Zbl 1466.65088 Appl. Math. Lett. 115, Article ID 106949, 8 p. (2021). MSC: 65M06 65N06 65M12 PDFBibTeX XMLCite \textit{A. Zlotnik} and \textit{R. Čiegis}, Appl. Math. Lett. 115, Article ID 106949, 8 p. (2021; Zbl 1466.65088) Full Text: DOI arXiv
Hieu, Le M.; Thanh, Dang N. H.; Surya Prasath, V. B. Second order monotone difference schemes with approximation on non-uniform grids for two-dimensional quasilinear parabolic convection-diffusion equations. (English. Russian original) Zbl 1460.65133 Vestn. St. Petersbg. Univ., Math. 53, No. 2, 232-240 (2020); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 2, 343-355 (2020). MSC: 65N06 65N12 65M22 35K58 PDFBibTeX XMLCite \textit{L. M. Hieu} et al., Vestn. St. Petersbg. Univ., Math. 53, No. 2, 232--240 (2020; Zbl 1460.65133); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 2, 343--355 (2020) Full Text: DOI
Li, Xiaoli; Rui, Hongxing Stability and convergence of characteristic MAC scheme and post-processing for the Oseen equations on non-uniform grids. (English) Zbl 1428.76136 Appl. Math. Comput. 342, 94-111 (2019). MSC: 76M20 65M06 65M12 65M15 65M25 76D07 PDFBibTeX XMLCite \textit{X. Li} and \textit{H. Rui}, Appl. Math. Comput. 342, 94--111 (2019; Zbl 1428.76136) Full Text: DOI
Sun, Yue; Rui, Hongxing Stability and convergence of the mark and cell finite difference scheme for Darcy-Stokes-Brinkman equations on non-uniform grids. (English) Zbl 1416.76191 Numer. Methods Partial Differ. Equations 35, No. 2, 509-527 (2019). MSC: 76M20 65N06 65N12 65N15 76S05 35Q35 PDFBibTeX XMLCite \textit{Y. Sun} and \textit{H. Rui}, Numer. Methods Partial Differ. Equations 35, No. 2, 509--527 (2019; Zbl 1416.76191) Full Text: DOI
Soori, Z.; Aminataei, A. A new approximation to Caputo-type fractional diffusion and advection equations on non-uniform meshes. (English) Zbl 1462.65114 Appl. Numer. Math. 144, 21-41 (2019). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{Z. Soori} and \textit{A. Aminataei}, Appl. Numer. Math. 144, 21--41 (2019; Zbl 1462.65114) Full Text: DOI
Zlotnik, Alexander On \(L^2\)-dissipativity of linearized explicit finite-difference schemes with a regularization on a non-uniform spatial mesh for the 1D gas dynamics equations. (English) Zbl 1411.65118 Appl. Math. Lett. 92, 115-120 (2019). MSC: 65M06 76M20 76N15 65M12 PDFBibTeX XMLCite \textit{A. Zlotnik}, Appl. Math. Lett. 92, 115--120 (2019; Zbl 1411.65118) Full Text: DOI
Li, Xiaoli; Rui, Hongxing; Chen, Shuangshuang Stability and superconvergence of efficient MAC schemes for fractional Stokes equation on non-uniform grids. (English) Zbl 1435.76051 Appl. Numer. Math. 138, 30-53 (2019). Reviewer: Abdallah Bradji (Annaba) MSC: 76M20 76D07 65M06 65M12 26A33 PDFBibTeX XMLCite \textit{X. Li} et al., Appl. Numer. Math. 138, 30--53 (2019; Zbl 1435.76051) Full Text: DOI
Sun, Yue; Rui, Hongxing MAC finite difference scheme for Stokes equations with damping on non-uniform grids. (English) Zbl 1409.76092 Comput. Math. Appl. 75, No. 4, 1272-1287 (2018). MSC: 76M20 65N06 65N12 PDFBibTeX XMLCite \textit{Y. Sun} and \textit{H. Rui}, Comput. Math. Appl. 75, No. 4, 1272--1287 (2018; Zbl 1409.76092) Full Text: DOI
Matus, Piotr; Poliakov, Dmitriy; Hieu, Le Minh On the consistent two-side estimates for the solutions of quasilinear convection-diffusion equations and their approximations on non-uniform grids. (English) Zbl 1432.65123 J. Comput. Appl. Math. 340, 571-581 (2018). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{P. Matus} et al., J. Comput. Appl. Math. 340, 571--581 (2018; Zbl 1432.65123) Full Text: DOI
Soori, Z.; Aminataei, A. Sixth-order non-uniform combined compact difference scheme for multi-term time fractional diffusion-wave equation. (English) Zbl 1393.65017 Appl. Numer. Math. 131, 72-94 (2018). MSC: 65M06 35R11 26A33 PDFBibTeX XMLCite \textit{Z. Soori} and \textit{A. Aminataei}, Appl. Numer. Math. 131, 72--94 (2018; Zbl 1393.65017) Full Text: DOI
Zlotnik, Alexander; Čiegis, Raimondas A “converse” stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation. (English) Zbl 1393.65019 Appl. Math. Lett. 80, 35-40 (2018). MSC: 65M06 35Q41 65M12 65M15 PDFBibTeX XMLCite \textit{A. Zlotnik} and \textit{R. Čiegis}, Appl. Math. Lett. 80, 35--40 (2018; Zbl 1393.65019) Full Text: DOI arXiv
Jha, Navnit; Gopal, Venu; Singh, Bhagat A family of compact finite difference formulations for three-space dimensional nonlinear Poisson’s equations in Cartesian coordinates. (English) Zbl 1387.35165 Differ. Equ. Dyn. Syst. 26, No. 1-3, 105-123 (2018). MSC: 35J25 35J60 35J65 65N06 PDFBibTeX XMLCite \textit{N. Jha} et al., Differ. Equ. Dyn. Syst. 26, No. 1--3, 105--123 (2018; Zbl 1387.35165) Full Text: DOI
Matus, P. P.; Hieu, Le Minh Monotone difference schemes on non-uniform grids for 2d quasi-linear parabolic convection-diffusion equation. (Russian. English summary) Zbl 1372.65238 Dokl. Nats. Akad. Nauk Belarusi 61, No. 4, 7-13 (2017). MSC: 65M06 35K57 PDFBibTeX XMLCite \textit{P. P. Matus} and \textit{L. M. Hieu}, Dokl. Nats. Akad. Nauk Belarusi 61, No. 4, 7--13 (2017; Zbl 1372.65238) Full Text: Link
Jha, Navnit; Kumar, Neelesh; Sharma, Kapil K. A third (four) order accurate, nine-point compact scheme for mildly-nonlinear elliptic equations in two space variables. (English) Zbl 1371.65111 Differ. Equ. Dyn. Syst. 25, No. 2, 223-237 (2017). MSC: 65N06 35J60 65N15 65N12 65N50 PDFBibTeX XMLCite \textit{N. Jha} et al., Differ. Equ. Dyn. Syst. 25, No. 2, 223--237 (2017; Zbl 1371.65111) Full Text: DOI
Liu, Li-Bin; Chen, Yanping A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection-diffusion problems. (English) Zbl 1353.65087 J. Comput. Appl. Math. 313, 152-167 (2017). MSC: 65L70 65L11 34B15 34E15 65L12 65L50 65L10 PDFBibTeX XMLCite \textit{L.-B. Liu} and \textit{Y. Chen}, J. Comput. Appl. Math. 313, 152--167 (2017; Zbl 1353.65087) Full Text: DOI
Matus, Piotr; Hieu, Le Minh; Vulkov, Lubin G. Analysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations. (English) Zbl 1348.65118 J. Comput. Appl. Math. 310, 186-199 (2017). MSC: 65M06 35K59 65M15 65M50 PDFBibTeX XMLCite \textit{P. Matus} et al., J. Comput. Appl. Math. 310, 186--199 (2017; Zbl 1348.65118) Full Text: DOI
Li, Tian; Wang, Caihua; Zheng, Shangkun Finite difference scheme on non-uniform mesh for two-dimensional singularly perturbed problems. (Chinese. English summary) Zbl 1363.65184 J. Tianjin Norm. Univ., Nat. Sci. Ed. 36, No. 3, 8-12 (2016). MSC: 65N06 65N15 35B25 35J25 65N50 PDFBibTeX XMLCite \textit{T. Li} et al., J. Tianjin Norm. Univ., Nat. Sci. Ed. 36, No. 3, 8--12 (2016; Zbl 1363.65184)
Sengupta, Tapan K.; Sengupta, Aditi A new alternating bi-diagonal compact scheme for non-uniform grids. (English) Zbl 1349.76139 J. Comput. Phys. 310, 1-25 (2016). MSC: 76F65 76M20 65M06 PDFBibTeX XMLCite \textit{T. K. Sengupta} and \textit{A. Sengupta}, J. Comput. Phys. 310, 1--25 (2016; Zbl 1349.76139) Full Text: DOI
Cravero, I.; Semplice, M. On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes. (English) Zbl 1343.65116 J. Sci. Comput. 67, No. 3, 1219-1246 (2016). Reviewer: Marius Ghergu (Dublin) MSC: 65M08 65M06 65M50 35L65 65M12 PDFBibTeX XMLCite \textit{I. Cravero} and \textit{M. Semplice}, J. Sci. Comput. 67, No. 3, 1219--1246 (2016; Zbl 1343.65116) Full Text: DOI arXiv
Zhao, Lijing; Deng, Weihua High order finite difference methods on non-uniform meshes for space fractional operators. (English) Zbl 1347.65130 Adv. Comput. Math. 42, No. 2, 425-468 (2016). Reviewer: Fernando Casas (Castellon) MSC: 65L12 65L20 26A33 34E13 65L50 34A08 PDFBibTeX XMLCite \textit{L. Zhao} and \textit{W. Deng}, Adv. Comput. Math. 42, No. 2, 425--468 (2016; Zbl 1347.65130) Full Text: DOI arXiv
Moisseyeva, Ye.; Beketaeva, A. Development of ENO scheme on non-uniform grid for simulation of supersonic flow of multispecies gas mixture. (Russian. English summary) Zbl 1474.65284 Mat. Zh. 15, No. 4, 78-93 (2015). MSC: 65M06 76J20 76N15 PDFBibTeX XMLCite \textit{Ye. Moisseyeva} and \textit{A. Beketaeva}, Mat. Zh. 15, No. 4, 78--93 (2015; Zbl 1474.65284)
Tian, Fang A high-order compact exponential-type finite difference scheme on non-uniform grid for convection-diffusion equation. (Chinese. English summary) Zbl 1349.65337 Math. Pract. Theory 45, No. 4, 268-275 (2015). MSC: 65M06 65M50 35K20 76R10 76R50 76M20 PDFBibTeX XMLCite \textit{F. Tian}, Math. Pract. Theory 45, No. 4, 268--275 (2015; Zbl 1349.65337)
Asthana, K.; Sengupta, T. K. An explicit higher order difference scheme on a compact stencil for elliptic equations on curvilinear geometries. (English) Zbl 1337.65134 Appl. Math. Comput. 242, 143-158 (2014). MSC: 65N06 35K57 76M20 PDFBibTeX XMLCite \textit{K. Asthana} and \textit{T. K. Sengupta}, Appl. Math. Comput. 242, 143--158 (2014; Zbl 1337.65134) Full Text: DOI
Huang, Xuefang; Guo, Rui; Ge, Yongbin A high accuracy compact difference scheme on non-uniform grids for the 1D unsteady convection diffusion equations. (Chinese. English summary) Zbl 1313.65218 Chin. J. Eng. Math. 31, No. 3, 371-380 (2014). MSC: 65M06 65M50 65M12 35K20 PDFBibTeX XMLCite \textit{X. Huang} et al., Chin. J. Eng. Math. 31, No. 3, 371--380 (2014; Zbl 1313.65218) Full Text: DOI
Sun, Jianan; Jia, Wei; Wu, Guangzhi A higher accurate compact difference scheme on non-uniform grid. (Chinese. English summary) Zbl 1313.65226 J. Northwest Norm. Univ., Nat. Sci. 50, No. 4, 31-35, 40 (2014). MSC: 65M06 65M50 35Q53 35K20 65M15 PDFBibTeX XMLCite \textit{J. Sun} et al., J. Northwest Norm. Univ., Nat. Sci. 50, No. 4, 31--35, 40 (2014; Zbl 1313.65226)
Christov, Christo I. Numerical implementation of the asymptotic boundary conditions for steadily propagating 2D solitons of Boussinesq type equations. (English) Zbl 1320.76031 Math. Comput. Simul. 82, No. 6, 1079-1092 (2012). MSC: 76D05 65M06 76M20 PDFBibTeX XMLCite \textit{C. I. Christov}, Math. Comput. Simul. 82, No. 6, 1079--1092 (2012; Zbl 1320.76031) Full Text: DOI
Cao, Guangman; Wang, Caihua; Qi, Haitao A non-uniform finite difference scheme for convection-diffusion equations. (Chinese. English summary) Zbl 1240.65311 J. Tianjin Norm. Univ., Nat. Sci. Ed. 30, No. 1, 7-10 (2010). MSC: 65N06 35J25 65N15 PDFBibTeX XMLCite \textit{G. Cao} et al., J. Tianjin Norm. Univ., Nat. Sci. Ed. 30, No. 1, 7--10 (2010; Zbl 1240.65311)
Amiraliyeva, I. G. Difference schemes for singularly perturbed Boussinesq system. (English) Zbl 1201.65147 Int. J. Appl. Math. 23, No. 2, 277-291 (2010). Reviewer: Damian Słota (Gliwice) MSC: 65M06 65M12 65M15 65M50 35Q35 35B25 PDFBibTeX XMLCite \textit{I. G. Amiraliyeva}, Int. J. Appl. Math. 23, No. 2, 277--291 (2010; Zbl 1201.65147)
Wang, Xuan; Yang, Zhifeng; Huang, Gordon; Chen, Bin A high-order compact difference scheme for 2D Laplace and Poisson equations in non-uniform grid systems. (English) Zbl 1221.65289 Commun. Nonlinear Sci. Numer. Simul. 14, No. 2, 379-398 (2009). MSC: 65N06 PDFBibTeX XMLCite \textit{X. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 14, No. 2, 379--398 (2009; Zbl 1221.65289) Full Text: DOI
Tian, Fang; Tian, Zhenfu A high accuracy compact difference scheme for convection diffusion reaction equation on non-uniform grid. (Chinese. English summary) Zbl 1212.65328 Chin. J. Eng. Math. 26, No. 2, 219-225 (2009). MSC: 65M06 65M12 65M50 35K57 PDFBibTeX XMLCite \textit{F. Tian} and \textit{Z. Tian}, Chin. J. Eng. Math. 26, No. 2, 219--225 (2009; Zbl 1212.65328)
Sun, Zhi-zhong A second order accurate difference scheme for the hyperbolic problem with concentrated data. (English) Zbl 1233.65061 Margenov, Svetozar (ed.) et al., Numerical analysis and its applications. 4th international conference, NAA 2008, Lozenetz, Bulgaria, June 16–20, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-00463-6/pbk). Lecture Notes in Computer Science 5434, 556-563 (2009). MSC: 65M06 35L15 PDFBibTeX XMLCite \textit{Z.-z. Sun}, Lect. Notes Comput. Sci. 5434, 556--563 (2009; Zbl 1233.65061) Full Text: DOI
Si, Haiqing; Wang, Tongguang Grid-optimized upwind dispersion-relation-preserving scheme on non-uniform Cartesian grids for computational aeroacoustics. (English) Zbl 1273.76299 Aerosp. Sci. Technol. 12, No. 8, 608-617 (2008). MSC: 76M20 76Q05 PDFBibTeX XMLCite \textit{H. Si} and \textit{T. Wang}, Aerosp. Sci. Technol. 12, No. 8, 608--617 (2008; Zbl 1273.76299) Full Text: DOI Link
Amiraliyev, G. M.; Amiraliyeva, I. G. Difference schemes for the singularly perturbed Sobolev equations. (English) Zbl 1127.65057 Elaydi, S. (ed.) et al., Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25–30, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-643-0/hbk). 23-40 (2007). MSC: 65M06 65M15 65M50 35K70 65M12 PDFBibTeX XMLCite \textit{G. M. Amiraliyev} and \textit{I. G. Amiraliyeva}, in: Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25--30, 2005. Hackensack, NJ: World Scientific. 23--40 (2007; Zbl 1127.65057)
Pandit, Swapan K.; Kalita, Jiten C.; Dalal, D. C. A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular. (English) Zbl 1343.76035 J. Comput. Phys. 225, No. 1, 1100-1124 (2007). MSC: 76M20 76D05 65M06 PDFBibTeX XMLCite \textit{S. K. Pandit} et al., J. Comput. Phys. 225, No. 1, 1100--1124 (2007; Zbl 1343.76035) Full Text: DOI
Kadalbajoo, Mohan K.; Ramesh, V. P. Hybrid method for numerical solution of singularly perturbed delay differential equations. (English) Zbl 1120.65088 Appl. Math. Comput. 187, No. 2, 797-814 (2007). Reviewer: Fuhua Ling (Milpitas) MSC: 65L10 34K10 65L12 65L50 34K28 34K26 PDFBibTeX XMLCite \textit{M. K. Kadalbajoo} and \textit{V. P. Ramesh}, Appl. Math. Comput. 187, No. 2, 797--814 (2007; Zbl 1120.65088) Full Text: DOI
Lu, Chang-Gen; Cao, Wei-Dong; Qian, Jian-Hua A study on numerical method of Navier-Stokes equation and nonlinear evolution of the coherent structures in a laminar boundary layer. (English) Zbl 1203.76100 J. Hydrodyn., Ser. B 18, No. 3, 372-377 (2006). MSC: 76M20 76D05 76D10 PDFBibTeX XMLCite \textit{C.-G. Lu} et al., J. Hydrodyn., Ser. B 18, No. 3, 372--377 (2006; Zbl 1203.76100) Full Text: DOI
Il’in, V. P.; Shmakov, I. A. On the finite volume solution of a 1D parabolic nonlinear equation. (English) Zbl 1249.65184 Bull. Novosib. Comput. Cent., Ser. Numer. Anal. 13, 33-42 (2005). MSC: 65M08 35K55 65M06 65M50 65M15 PDFBibTeX XMLCite \textit{V. P. Il'in} and \textit{I. A. Shmakov}, Bull. Novosib. Comput. Cent., Ser. Numer. Anal. 13, 33--42 (2005; Zbl 1249.65184)
Amiraliyev, G. M. The convergence of a finite difference method on layer-adapted mesh for a singularly perturbed system. (English) Zbl 1068.65099 Appl. Math. Comput. 162, No. 3, 1023-1034 (2005). Reviewer: Narahari Parhi (Bhubaneswar) MSC: 65L12 65L20 34B15 34E15 65L60 65L10 PDFBibTeX XMLCite \textit{G. M. Amiraliyev}, Appl. Math. Comput. 162, No. 3, 1023--1034 (2005; Zbl 1068.65099) Full Text: DOI
Ma, Yanwen; Gao, Hui; Fu, Dexun; Li, Xinliang Difference schemes on non-uniform mesh and their application. (English) Zbl 1161.76528 Prog. Nat. Sci. 14, No. 10, 848-854 (2004). MSC: 76M20 PDFBibTeX XMLCite \textit{Y. Ma} et al., Prog. Nat. Sci. 14, No. 10, 848--854 (2004; Zbl 1161.76528) Full Text: DOI
Esfahanian, V.; Ghader, S.; Ashrafi, Kh. Accuracy analysis of super compact scheme on non-uniform grid with application to parabolized stability equations. (English) Zbl 1060.76615 Int. J. Numer. Methods Fluids 46, No. 5, 485-505 (2004). MSC: 76M20 76E05 65M15 PDFBibTeX XMLCite \textit{V. Esfahanian} et al., Int. J. Numer. Methods Fluids 46, No. 5, 485--505 (2004; Zbl 1060.76615) Full Text: DOI
Morinishi, Youhei; Vasilyev, Oleg V.; Ogi, Takeshi Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations. (English) Zbl 1079.76602 J. Comput. Phys. 197, No. 2, 686-710 (2004). MSC: 76M20 PDFBibTeX XMLCite \textit{Y. Morinishi} et al., J. Comput. Phys. 197, No. 2, 686--710 (2004; Zbl 1079.76602) Full Text: DOI
Amiraliyev, G. M. Uniform numerical method for a quasilinear system with boundary layer. (English) Zbl 1032.65517 Simos, T. E. (ed.), Computational methods in sciences and engineering 2003 (ICCMSE 2003). Proceedings of the international conference, Kastoria, Greece, September 12-16, 2003. River Edge, NJ: World Scientific. 16-21 (2003). MSC: 65L10 65L20 34B15 34E15 65L12 PDFBibTeX XMLCite \textit{G. M. Amiraliyev}, in: Computational methods in sciences and engineering 2003 (ICCMSE 2003). Proceedings of the international conference, Kastoria, Greece, September 12--16, 2003. River Edge, NJ: World Scientific. 16--21 (2003; Zbl 1032.65517)
Elbarbary, Elsayed M. E.; El-Kady, M. Chebyshev finite difference approximation for the boundary value problems. (English) Zbl 1027.65098 Appl. Math. Comput. 139, No. 2-3, 513-523 (2003). MSC: 65L10 65L12 34B05 34B15 PDFBibTeX XMLCite \textit{E. M. E. Elbarbary} and \textit{M. El-Kady}, Appl. Math. Comput. 139, No. 2--3, 513--523 (2003; Zbl 1027.65098) Full Text: DOI
Zhukov, V. T.; Strakhovskaya, L. G.; Fedorenko, R. P.; Feodoritova, O. B. On an approach to construct finite-difference schemes. (Russian, English) Zbl 1057.76047 Zh. Vychisl. Mat. Mat. Fiz. 42, No. 2, 222-234 (2002); translation in Comput. Math. Math. Phys. 42, No. 2, 211-223 (2002). Reviewer: Andrei Zemskov (Moskva) MSC: 76M20 35Q30 35Q05 35B27 PDFBibTeX XMLCite \textit{V. T. Zhukov} et al., Zh. Vychisl. Mat. Mat. Fiz. 42, No. 2, 222--234 (2002; Zbl 1057.76047); translation in Comput. Math. Math. Phys. 42, No. 2, 211--223 (2002)
Haddad, O. M.; Al-Nimr, M. A.; Abu-Ayyad, M. A. Numerical simulation of forced convection flow past a parabolic cylinder embedded in porous medium. (English) Zbl 1010.76078 Int. J. Numer. Methods Heat Fluid Flow 12, No. 1, 6-28 (2002). MSC: 76R05 76S05 76M20 80A20 PDFBibTeX XMLCite \textit{O. M. Haddad} et al., Int. J. Numer. Methods Heat Fluid Flow 12, No. 1, 6--28 (2002; Zbl 1010.76078) Full Text: DOI
Gracia, J. L.; Clavero, C.; Lisbona, F. Numerical approximation of convection-diffusion problems using an improved upwind scheme on a Shishkin mesh. (Spanish) Zbl 0993.65116 Cruz Lopez de Silanes, Maria (ed.) et al., Actes des 6èmes journées Zaragoza-Pau de mathématiques appliquées et de statistiques. Pau: Publications de Université de Pau et Pays de l’Adour, PUP. 289-296 (2001). MSC: 65N06 35B25 65N12 35J25 65N50 PDFBibTeX XMLCite \textit{J. L. Gracia} et al., in: Actes des 6èmes journées Zaragoza-Pau de mathématiques appliquées et de statistiques. Pau: Publications de Université de Pau et Pays de l'Adour, PUP. 289--296 (2001; Zbl 0993.65116)
Duvnjaković, Enes A variational difference scheme for a singularly perturbed one-dimensional reaction-diffusion problem. (English) Zbl 0992.65085 Rad. Mat. 10, No. 1, 109-119 (2001). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65L10 65L60 65L12 34B05 34E15 PDFBibTeX XMLCite \textit{E. Duvnjaković}, Rad. Mat. 10, No. 1, 109--119 (2001; Zbl 0992.65085)
Al Moatassime, Hassan; Jouron, Claude A multigrid method for solving steady viscoelastic fluid flow. (English) Zbl 1020.76034 Comput. Methods Appl. Mech. Eng. 190, No. 31, 4061-4080 (2001). MSC: 76M20 76A10 PDFBibTeX XMLCite \textit{H. Al Moatassime} and \textit{C. Jouron}, Comput. Methods Appl. Mech. Eng. 190, No. 31, 4061--4080 (2001; Zbl 1020.76034) Full Text: DOI
Haddad, O. M.; Abu-Qudais, M.; Abu-Hijleh, Bassam A. K.; Maqableh, A. M. Entropy generation due to laminar forced convection flow past a parabolic cylinder. (English) Zbl 0998.76081 Int. J. Numer. Methods Heat Fluid Flow 10, No. 7, 770-779 (2000). MSC: 76R10 76M20 80A20 PDFBibTeX XMLCite \textit{O. M. Haddad} et al., Int. J. Numer. Methods Heat Fluid Flow 10, No. 7, 770--779 (2000; Zbl 0998.76081) Full Text: DOI
Chou, Mo-Hong A multigrid finite difference approach to steady flow between eccentric rotating cylinders. (English) Zbl 0992.76067 Int. J. Numer. Methods Fluids 34, No. 6, 479-494 (2000). MSC: 76M20 76U05 65N55 PDFBibTeX XMLCite \textit{M.-H. Chou}, Int. J. Numer. Methods Fluids 34, No. 6, 479--494 (2000; Zbl 0992.76067) Full Text: DOI
Fournié, Michel High order conservative difference methods for 2D drift-diffusion model on non-uniform grid. (English) Zbl 0959.82033 Appl. Numer. Math. 33, No. 1-4, 381-392 (2000). MSC: 82D37 82C80 65N06 76M20 PDFBibTeX XMLCite \textit{M. Fournié}, Appl. Numer. Math. 33, No. 1--4, 381--392 (2000; Zbl 0959.82033) Full Text: DOI
Haddad, O. M.; Abu-Qudais, M.; Maqableh, A. M. Numerical solutions of the Navier-Stokes and energy equations for laminar incompressible flow past parabolic bodies. (English) Zbl 0973.76586 Int. J. Numer. Methods Heat Fluid Flow 10, No. 1, 80-93 (2000). MSC: 76M20 76D05 80A20 PDFBibTeX XMLCite \textit{O. M. Haddad} et al., Int. J. Numer. Methods Heat Fluid Flow 10, No. 1, 80--93 (2000; Zbl 0973.76586) Full Text: DOI
Mackenzie, John Uniform convergence analysis of an upwind finite-difference approximation of a convection-diffusion boundary value problem on an adaptive grid. (English) Zbl 0929.65047 IMA J. Numer. Anal. 19, No. 2, 233-249 (1999). Reviewer: Marco Marletta (Leicester) MSC: 65L10 65L12 34B05 65L50 34E15 PDFBibTeX XMLCite \textit{J. Mackenzie}, IMA J. Numer. Anal. 19, No. 2, 233--249 (1999; Zbl 0929.65047) Full Text: DOI Link
Zhong, Wanxie; Zhuang, Xinglai; Zhu, Jianping A self-adaptive time integration algorithm for solving partial differential equations. (English) Zbl 0907.65081 Appl. Math. Comput. 89, No. 1-3, 295-312 (1998). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M06 65M12 35K15 35Q53 PDFBibTeX XMLCite \textit{W. Zhong} et al., Appl. Math. Comput. 89, No. 1--3, 295--312 (1998; Zbl 0907.65081) Full Text: DOI
de Arruda Mancera, P. F.; Hunt, R. Fourth-order method for solving the Navier-Stokes equations in a constricting channel. (English) Zbl 0935.76061 Int. J. Numer. Methods Fluids 25, No. 10, 1119-1135 (1997). Reviewer: W.L.Chow (Boca Raton) MSC: 76M20 76D05 PDFBibTeX XMLCite \textit{P. F. de Arruda Mancera} and \textit{R. Hunt}, Int. J. Numer. Methods Fluids 25, No. 10, 1119--1135 (1997; Zbl 0935.76061) Full Text: DOI
Orlandi, P.; Fatica, M. Direct simulations of turbulent flow in a pipe rotating about its axis. (English) Zbl 0901.76047 J. Fluid Mech. 343, 43-72 (1997). MSC: 76M20 76F10 76U05 PDFBibTeX XMLCite \textit{P. Orlandi} and \textit{M. Fatica}, J. Fluid Mech. 343, 43--72 (1997; Zbl 0901.76047) Full Text: DOI
Armenio, Vincenzo An improved MAC method (SIMAC) for unsteady high-Reynolds free surface flows. (English) Zbl 0893.76048 Int. J. Numer. Methods Fluids 24, No. 2, 185-214 (1997). MSC: 76M20 76D05 PDFBibTeX XMLCite \textit{V. Armenio}, Int. J. Numer. Methods Fluids 24, No. 2, 185--214 (1997; Zbl 0893.76048) Full Text: DOI
Ostapenko, V. V. Difference schemes of the balance method on a non-uniform mesh. (English. Russian original) Zbl 0852.65079 Comput. Math. Math. Phys. 35, No. 6, 709-717 (1995); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 6, 893-904 (1995). MSC: 65M06 35L65 PDFBibTeX XMLCite \textit{V. V. Ostapenko}, Comput. Math. Math. Phys. 35, No. 6, 709--717 (1995; Zbl 0852.65079); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 6, 893--904 (1995)
Degtyarëv, S. L. The stability of difference schemes with variable weights for the one- dimensional heat-conduction equation. (English. Russian original) Zbl 0832.65100 Comput. Math. Math. Phys. 34, No. 8-9, 1141-1146 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 8-9, 1316-1322 (1994). MSC: 65M12 65M06 35K05 PDFBibTeX XMLCite \textit{S. L. Degtyarëv}, Comput. Math. Math. Phys. 34, No. 8--9, 1141--1146 (1994; Zbl 0832.65100); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 8--9, 1316--1322 (1994)
Makarov, V. L.; Guminskij, V. V. A three-point scheme of higher-order accuracy for a system of second- order ordinary differential equations (nonself-adjoint case). (English. Russian original) Zbl 0823.65078 Differ. Equations 30, No. 3, 457-465 (1994); translation from Differ. Uravn. 30, No. 3, 493-502 (1994). Reviewer: V.Chernyatin (Szczecin) MSC: 65L10 65L20 65L50 65L12 34B05 PDFBibTeX XMLCite \textit{V. L. Makarov} and \textit{V. V. Guminskij}, Differ. Equations 30, No. 3, 1 (1994; Zbl 0823.65078); translation from Differ. Uravn. 30, No. 3, 493--502 (1994)
Majkov, A. R.; Sveshnikov, A. G. Conservative difference schemes for non-stationary Maxwell’s equations in three dimensions. (English. Russian original) Zbl 0817.65131 Comput. Math. Math. Phys. 33, No. 9, 1195-1206 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 9, 1352-1367 (1993). MSC: 65Z05 65M12 65M06 35Q60 78A25 PDFBibTeX XMLCite \textit{A. R. Majkov} and \textit{A. G. Sveshnikov}, Comput. Math. Math. Phys. 33, No. 9, 1352--1367 (1993; Zbl 0817.65131); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 9, 1352--1367 (1993)
Bakaev, N. Yu. Some problems of well-posedness of difference schemes on non-uniform grids. (English. Russian original) Zbl 0811.65067 Comput. Math. Math. Phys. 33, No. 4, 511-524 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 4, 561-577 (1993). Reviewer: S.Burys (Kraków) MSC: 65M06 65L05 65M12 65M15 34G10 35L15 PDFBibTeX XMLCite \textit{N. Yu. Bakaev}, Comput. Math. Math. Phys. 33, No. 4, 561--577 (1993; Zbl 0811.65067); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 4, 561--577 (1993)
Ramakrishna, K.; Cohen, I. M.; Ayyaswamy, P. S. Numerical methods for two-dimensional analysis of electrical breakdown in a non-uniform gap. (English) Zbl 0766.65111 J. Comput. Phys. 104, No. 1, 173-184 (1993). Reviewer: E.V.Nicolau (Bucureşti) MSC: 65Z05 65M06 35Q60 78M20 78A55 PDFBibTeX XMLCite \textit{K. Ramakrishna} et al., J. Comput. Phys. 104, No. 1, 173--184 (1993; Zbl 0766.65111) Full Text: DOI
Wu, Qiguang; Li, Jichun Numerical methods for parabolic equation with a small parameter in time variable. (English) Zbl 0757.65099 Appl. Math. Mech., Engl. Ed. 12, No. 8, 733-739 (1991). Reviewer: L.G.Vulkov (Russe) MSC: 65M06 65M12 35K15 PDFBibTeX XMLCite \textit{Q. Wu} and \textit{J. Li}, Appl. Math. Mech., Engl. Ed. 12, No. 8, 733--739 (1991; Zbl 0757.65099) Full Text: DOI
Glaister, P. A TVD finite difference scheme with non-uniform meshes and without upstream weighting. (English) Zbl 0732.76056 Comput. Math. Appl. 22, No. 3, 45-58 (1991). MSC: 76M20 76B99 PDFBibTeX XMLCite \textit{P. Glaister}, Comput. Math. Appl. 22, No. 3, 45--58 (1991; Zbl 0732.76056) Full Text: DOI
Ashirov, B. S. On numerical solution of nonlocal boundary value problems for equations with singular coefficients. (Russian. English summary) Zbl 0711.65063 Izv. Akad. Nauk Turkm. SSR, Ser. Fiz.-Tekh. Khim. Geol. Nauk 1990, No. 3, 9-16 (1990). Reviewer: T.Mitsui MSC: 65L10 34B15 PDFBibTeX XMLCite \textit{B. S. Ashirov}, Izv. Akad. Nauk Turkm. SSR, Ser. Fiz.-Tekh., Khim. Geol. Nauk 1990, No. 3, 9--16 (1990; Zbl 0711.65063)
Choi, Hae Cheon; Song, Jin Ho; Yoo, Jung Yul Numerical simulation of the planar contraction flow of a Giesekus fluid. (English) Zbl 0669.76017 J. Non-Newtonian Fluid Mech. 29, 347-379 (1988). MSC: 76A05 76M99 PDFBibTeX XMLCite \textit{H. C. Choi} et al., J. Non-Newton. Fluid Mech. 29, 347--379 (1988; Zbl 0669.76017) Full Text: DOI
Lonsdale, G. Solution of a rotating Navier-Stokes problem by a nonlinear multigrid algorithm. (English) Zbl 0596.76113 GMD-Stud. 110, 85-99 (1986). MSC: 76U05 76D05 65N06 PDFBibTeX XML
Kalis, Kh. Eh. On the application of some monotone difference schemes for the solution of second order elliptic equations. (Russian) Zbl 0576.65098 Chislennye Metody Mekh. Sploshnoj Sredy 16, No. 2, 65-80 (1985). MSC: 65N06 35J25 65L10 PDFBibTeX XML
Sobey, R. J. An optimized solution for the diffusion equation on a non-uniform grid. (English) Zbl 0531.65051 Int. J. Numer. Methods Eng. 20, 465-477 (1984). MSC: 65N22 65N06 35K05 65F10 PDFBibTeX XMLCite \textit{R. J. Sobey}, Int. J. Numer. Methods Eng. 20, 465--477 (1984; Zbl 0531.65051) Full Text: DOI
Gane, C. R.; Oliver, A. J.; Soulsby, D. R.; Stephenson, P. L. Numerical solution of coupled conduction-convection problems using lumped-parameter methods. (English) Zbl 0557.76003 Numerical methods in heat transfer, 2nd int. Conf., Venice/Italy 1981, Vol. 2, 227-274 (1983). Reviewer: H.K.Verma MSC: 76M99 80A20 PDFBibTeX XML
Trottier, Jacques J.; Unny, T. E.; Al-Nassri, S. A.; Chandrasekhar, M. Two dimension-curvilinear grid for open channel flow simulation. (English) Zbl 0517.76037 Appl. Math. Modelling 7, 48-56 (1983). MSC: 76D05 76-04 76M99 65C20 65N22 PDFBibTeX XMLCite \textit{J. J. Trottier} et al., Appl. Math. Modelling 7, 48--56 (1983; Zbl 0517.76037) Full Text: DOI
Fletcher, C. A. J.; Srinivas, K. Stream function vorticity revisited. (English) Zbl 0512.76037 Comput. Methods Appl. Mech. Eng. 41, 297-322 (1983). MSC: 76D05 76M99 65N30 PDFBibTeX XMLCite \textit{C. A. J. Fletcher} and \textit{K. Srinivas}, Comput. Methods Appl. Mech. Eng. 41, 297--322 (1983; Zbl 0512.76037) Full Text: DOI