数学与计算机科学 |
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奇异摄动问题在修正的Bakhvalov-Shishkin网格上的混合差分格式 |
郑权1, 刘颖1, 刘忠礼2 |
1.北方工业大学 理学院,北京 100144 2.北京联合大学 生物化学工程学院,北京 100023 |
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The hybrid finite difference schemes on the modified Bakhvalov-Shishkin mesh for the singularly perturbed problem |
ZHENG Quan1, LIU Ying1, LIU Zhongli2 |
1.College of Sciences, North China University of Technology, Beijing 100144, China 2.College of Biochemical Engineering, Beijing Union University, Beijing 100023, China |
1 ROOS H G, STYNES M, TOBISKA L . Robust Numerical Methods for Singularly Perturbed Differential Equations[M].2nd ed. Heidelberg: Springer-Verlag, 2008. 2 ROOS H G, LINβ T . Sufficient conditions for uniform convergence on layer-adapted grids[J]. Computing, 1999, 63(1): 27-45. 3 STYNES M, ROOS H G . The midpoint upwind scheme[J]. Applied Numerical Mathematics, 1997, 23(3): 361-374. DOI:10.1016/s0168-9274(96)00071-2 4 梁克维,李大明,江金生 . 中点迎风差分格式在Bakhvalov-Shishkin网格上的注记[J]. 浙江大学学报(理学版), 2002, 29(1): 20-24.DOI:10.3785/j.issn.1008-9497.2002.01.05 LIANG K W, LI D M, JIANG J S . Note on the midpoint upwind scheme of the Bakhvalov-Shishkin mesh[J]. Journal of Zhejiang University(Science Edition), 2002, 29(1): 20-24.DOI:10.3785/j.issn.1008-9497.2002.01.05 5 ZHENG Q, FENG X L, LI X Z . ε-uniform convergence of the midpoint upwind scheme on the Bakhvalov-Shishkin mesh for singularly perturbed problems[J]. Journal of Computational Analysis and Applications, 2014, 17(1): 40-47. 6 ZHENG Q, LI X Z, GAO Y . Uniformly convergent hybrid schemes for solutions and derivatives in quasilinear singularly perturbed BVPs[J]. Applied Numerical Mathematics, 2015, 91:46-59.DOI:10.1016/j.apnum.2014.12.010 7 GOWRISANKAR S, NATESAN S . Uniformly convergent numerical method for singularly perturbed parabolic initial-boundary-value problems with equidistributed grids[J]. International Journal of Computer Mathematics, 2014, 91(3):553-577.DOI:10.1080/00207160.2013.792925 8 DAS A, NATESAN S . Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection-diffusion problems on Shishkin mesh[J]. Applied Mathematics and Computation, 2015, 271(C): 168-186.DOI:10.1016/j.amc.2015.08.137 9 周琴 . 椭圆型奇异摄动问题差分格式的一致收敛性分析[J]. 数学杂志, 2015,35(4):933-940.DOI:10.13548/j.sxzz.2015.04.014 ZHOU Q . Analysis of uniform convergence for difference scheme of an elliptic singularly perturbed problem[J]. Journal of Mathematics, 2015, 35(4):933-940. DOI:10.13548/j.sxzz.2015.04.014 10 KADALBAJOO M K, PATIDAR K C . ε-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems[J]. Applied Mathematics and Computation, 2006, 179(1):248-266. DOI:10.1016/j.amc.2005.11.096 |
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