A Uniformly Convergent Numerical Method Using Weak Formulation for Singularly Perturbed Differential Equations

• 作者: Weiqun Zhang
• 来源期刊: 数学和系统科学:英文版
• 学科: 数学
• 关键词: SINGULAR PERTURBATION differential equations boundary layers numerical methods weak FORMULATION
• 年，卷（期）: 2019,（1）
• 页码范围: 1-6
• 页数: 6页
• 分类号: O1

摘要

A numerical method using weak formulation is proposed to solve singularly perturbed differential equations. The numerical method is applied to both linear and nonlinear perturbation problems. A linear differential equation is solved using its weak formulation with a test space composed of exponential functions matching boundary layers. A nonlinear singular perturbation problem is converted into a system of linear differentiation equations. Then each linear differential equation is solved iteratively. The uniform convergence, which is independent of the singular perturbation parameter, is numerically verified.