二维扩展Fisher-Kolmogorov方程的线性化紧差分格式的最大模误差分析 / On Maximum Norm Error Analysis of a Linearized Compact Difference Scheme for the 2D Extended Fisher-Kolmogorov Equation
- Resource Type
- Academic Journal
- Authors
- 李娟; 高广花; LI Juan; GAO Guang-hua
- Source
- 西南师范大学学报(自然科学版) / Journal of Southwest China Normal University(Natural Science Edition). 42(3):12-21
- Subject
- 二维扩展Fisher-Kolmogorov方程
紧差分格式
非线性问题
线性化
2D extend Fisher-Kolmogorov equation
compact difference scheme
nonlinear problem
linearization
- Language
- Chinese
- ISSN
- 1000-5471
利用降阶法给出二维扩展Fisher-Kolmogorov方程的三层线性化紧差分格式,证明了解的存在唯一性及在L∞范数下时间方向二阶收敛、空间方向四阶收敛.最后通过数值算例,验证差分格式是有效的.
This article is related to the maximum norm error analysis of a three level linearized compact difference scheme for the 2D extended Fisher-Kolmogorov equation.The unique solvability and unconditional convergence of the difference solution are proved.The convergence order is O(h4+τ2)in the maximum norm.Numerical examples are given to demonstrate the theoretical results.