非线性发展方程的小模板简化Padé格式

基金项目: 国家自然科学基金资助项目(10371118,90411009);中国科学技术大学火灾科学国家重点实验室基金资助项目;北京计算物理实验室基金资助项目

Small-Stencil Pad Schemes to Solve Nonlinear Evolution Equations

Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China

摘要: 在有理逼近的紧致格式的理论基础上，采用特别的统一的Padé逼近形式，构造了针对高阶非线性发展方程的、简单小模板的差商格式．不仅保持了格式的四阶精度，而且还可以采用追赶法求解得到的3对角矩阵，或者采用三阶Runge-Kutta法直接求解积分．计算效果通过多种算例表明是十分令人满意的．相对于其他差分格式，此方法具有模板较小而精度保持四阶的优点．
- 发展方程 /
- 紧致格式 /
- Padé逼近 /
- 节点模板 /
- 孤立子
Abstract: A set of small-stencil new Pad schemes with the same denominator are presented to solve high-order non-linear evoltuion equations. Using this scheme, the fourth-order precision cannot only be kept, but also the final three-diagonal discrete systems are solved by simple Doolittle methods, or ODE systems by Runge-Kutta technique. Numerical samples show that the schemes are very satisfactory. And the advantage of the schemes is very clear compared to other finite difference schemes.
- evolution equation /
- compact scheme /
- Pad scheme /
- node stencil /
- soliton

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