拟线性奇异摄动微分方程的自适应差分方法
Adaptive Difference Method for Quasilinear Singularly Perturbed Differential Equations
摘要:
利用简单迎风差分格式和自适应网格方法相结合求解拟线性奇异摄动方程两点边值问题，通过等分布弧长控制函数而产生自适应网格，得到自适应差分格式的关于摄动参数ε一致的一阶误差估计，最后数值算例验证数值解的一阶一致收敛性，表明该方法的可靠性与准确性。
Abstract:
A simple upwind difference scheme and an adaptive grid method are combined to solve the quasilinear singularly perturbed two-point boundary value problem. The adaptive mesh is generated by equally distributing the arc-length control function. The first-order error estimate of the adaptive difference scheme uniform with respect to the perturbation parameter ε is obtained. Finally, numerical examples are given to verify the uniform first-order convergence and show the reliability and accuracy of the method.
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