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- Title
A Compact Difference Scheme for One-dimensional Nonlinear Delay Reaction-diffusion Equations with Variable Coefficient.
- Authors
Jianqiang Xie; Dingwen Deng; Huasheng Zheng
- Abstract
First of all, a compact difference scheme (CDS) is established for one-dimensional (1D) nonlinear reaction-diffusion equations (RDEs) with a fixed delay. By the energy method, it is proved that the difference solution converges to exact solution with a convergence order of O(τ² + h4) in L∞ - norm. Then, a Richardson extrapolation method (REM) is applied to make the final solution fourth-order accurate in both time and space. Besides, the extensions of the solver to other complex delay problems are studied in detail. Finally, numerical results demonstrate the high accuracy and efficiency of our algorithms.
- Subjects
REACTION-diffusion equations; STOCHASTIC convergence; RICHARDSON extrapolation; NUMERICAL analysis; PARABOLIC differential equations
- Publication
IAENG International Journal of Applied Mathematics, 2017, Vol 47, Issue 1, p14
- ISSN
1992-9978
- Publication type
Article