Numerical Algorithms for Solving One Type of Singular Integro-Differential Equation Containing Derivatives of the Time Delay States

• 作者: Shihchung Chiang Terry L. Herdman
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Integro-Differential Equation of the Second Kind WEAKLY SINGULAR KERNEL Numerical Algorithms Rates of CONVERGENCE
• 年，卷（期）: 2015,（8）
• 页码范围: 1294-1301
• 页数: 8页
• 分类号: O1

摘要

This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly singular kernel. These equations are types of integro-differential equation of the second kind and were originally obtained from an aeroelasticity problem. One of the main contributions of this study is to propose numerical algorithms that do not involve transforming the original equation into the corresponding Volterra equation, but still enable the numerical solution of the original equation to be determined. The feasibility of the proposed numerical algorithm is demonstrated by applying examples in measuring the maximum errors with exact solutions at every computed nodes and calculating the corresponding numerical rates of convergence thereafter.