Spline solution of the generalized Burgers'-Fisher equation
作者： Reza Mohammadi
DOI: 10.1080/00036811.2011.596479
关键词: Spline (mathematics) 、 Numerical analysis 、 Exponential spline 、 Finite difference 、 Mathematics 、 Error analysis 、 M-spline 、 Fisher equation 、 Energy method 、 Mathematical analysis
摘要: A numerical method based on exponential spline and finite difference approximations is developed to solve the generalized Burgers'-Fisher equation. The error analysis, stability convergence properties of are studied via energy method. shown be unconditionally stable accurate orders 𝒪(k + kh + h 2) 4). Some test problems given demonstrate applicability purposed numerically. Numerical results verify theoretical behaviour properties. main superiority presented scheme its simplicity in comparison with existing well-known methods.
sci-hub.se 参考文章(35)
Jalil Rashidinia, Reza Mohammadi, Tension spline solution of nonlinear sine-Gordon equation Numerical Algorithms. ,vol. 56, pp. 129- 142 ,(2011) , 10.1007/S11075-010-9377-X
A. Golbabai, M. Javidi, A spectral domain decomposition approach for the generalized Burger’s–Fisher equation Chaos, Solitons & Fractals. ,vol. 39, pp. 385- 392 ,(2009) , 10.1016/J.CHAOS.2007.04.013
Doǧan Kaya, Salah M. El-Sayed, A numerical simulation and explicit solutions of the generalized Burgers-Fisher equation Applied Mathematics and Computation. ,vol. 152, pp. 403- 413 ,(2004) , 10.1016/S0096-3003(03)00565-4
Chun-Gang Zhu, Ren-Hong Wang, Numerical solution of Burgers–Fisher equation by cubic B-spline quasi-interpolation Applied Mathematics and Computation. ,vol. 216, pp. 2679- 2686 ,(2009) , 10.1016/J.AMC.2008.11.045
A. G. Bratsos, L. A. Petrakis, An explicit numerical scheme for the modified Burgers' equation International Journal for Numerical Methods in Biomedical Engineering. ,vol. 27, pp. 232- 237 ,(2011) , 10.1002/CNM.1294
Peter C. Chu, Chenwu Fan, A Three-Point Combined Compact Difference Scheme Journal of Computational Physics. ,vol. 140, pp. 370- 399 ,(1998) , 10.1006/JCPH.1998.5899
Mohammad Javidi, Spectral collocation method for the solution of the generalized Burger–Fisher equation Applied Mathematics and Computation. ,vol. 174, pp. 345- 352 ,(2006) , 10.1016/J.AMC.2005.04.084
Abdul-Majid Wazwaz, The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations Applied Mathematics and Computation. ,vol. 188, pp. 1467- 1475 ,(2007) , 10.1016/J.AMC.2006.11.013
Melvyn Ciment, Stephen H. Leventhal, Bernard C. Weinberg, The Operator Compact Implicit Method for Parabolic Equations Journal of Computational Physics. ,vol. 28, pp. 135- 166 ,(1978) , 10.1016/0021-9991(78)90031-1
Murat Sari, Gürhan Gürarslan, Asuman Zeytinoğlu, High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation International Journal for Numerical Methods in Biomedical Engineering. ,vol. 27, pp. 1296- 1308 ,(2011) , 10.1002/CNM.1360