Full-Discretized Numerical Methods for Solving a Class of Integro-Differential Equations of the First Kind

10.29428/9789860544169.201801.0040

蔣世中

integro-differential equations ； weakly singular kernel ； nonsingular kernel ； 微分積分並列方程式 ； 弱奇異核 ； 非奇異核

NCS 2017 全國計算機會議

2017（2018 / 01 / 01）

214 - 218

英文

This study presents full-discretized numerical algorithms for solving a class of integro-differential equations of the first kind. This class of equations consists of an integro-differential term containing an Abel-type kernel. First kind equations with a weakly singular kernel originated from an aeroelasticity problem. The authors propose full-discretized central difference numerical methods, central difference and center point (CC) and central difference and integration (CI), for equations with weakly singular kernels and obtain superior results by revising the numerical algorithms to create central difference, center point, and revision (CCR) and central difference, integration, and revision (CIR) for the corresponding equations with nonsingular kernels. The feasibility of the proposed numerical algorithms is demonstrated by applying them to examples in which the CPU times and maximum errors are compared with exact solutions.

本文將介紹數值方法求解微分積分並列方程式。方法CC及CI用於弱奇異核方程式，方法CCR及CIR則用於非奇異核方程式。