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多区间泰勒配置法求解一类线性Volterra积分-微分方程
马淑芳, 莱蒙, 钟霖
东北林业大学 理学院, 黑龙江 哈尔滨 150040
摘要:
考虑了一类线性Volterra积分-微分方程(VIDEs)的多区间泰勒配置解法,其主要技术是将求解线性VIDEs转化为求解线性代数方程组.该方法的优点是易于实现,适用于长时间的计算.采用基于残差函数的误差分析法分析了方法的误差,通过算例验证了所提出方法的适用性和有效性.
关键词:  线性Volterra积分-微分方程(VIDEs)  泰勒配置方法  多区间  近似解
DOI:10.3969/J.ISSN.1000-5137.2021.01.002
分类号:O241
基金项目:中央高校基本科研业务费专项资金项目(2572018BC19)
A multiple interval Taylor collocation method for a linear Volterra integro-differential equations
MA Shufang, JOKA Dengata-lemu, ZHONG Lin
College of Science, Northeast Forestry University, Harbin 150040, Heilongjiang, China
Abstract:
In this paper, we consider a multiple interval Taylor collocation method for a class of linear Volterra integro-differential equations(VIDEs). The main technique is to reduce the linear Volterra integro-differential equations(VIDEs) to a linear algebraic system. The advantage of this method is that it is easy to implement and suitable for long-time calculation. And we analyze the error of the method based on residual function. Finally, the applicability and effectiveness of the method are verified by an example.
Key words:  linear Volterra integro-differential equations(VIDEs)  Taylor collocation method  multiple interval  approximation solution