Piecewise barycentric interpolating functions for the numerical solution of Volterra integro-differential equations

被引：10

作者：

Torkaman, Soraya ^{[1
]}

Heydari, Mohammad ^{[1
]}

Loghmani, Ghasem Barid ^{[1
]}

机构：

[1] Yazd Univ, Dept Math, Yazd, Iran

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 10期

关键词：

convergence analysis; Floater-Hormann interpolant; operational matrices of integral and product; piecewise barycentric interpolating functions; Volterra integro-differential equations; BLOCK-PULSE FUNCTIONS; FREDHOLM INTEGRAL-EQUATIONS; BERNSTEIN POLYNOMIALS; CONVERGENCE ANALYSIS; FRACTIONAL-ORDER; POPULATION-MODEL; MULTI-WAVELETS; TAU-METHOD; HYBRID; ALGORITHM;

D O I：

10.1002/mma.8154

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This investigation presents an effective numerical scheme using a new set of basis functions, namely, the piecewise barycentric interpolating functions, to find the approximate solution of Volterra integro-differential equations (VIDEs). The operational matrices of integration and product for the PBIFs are provided. Then these operational matrices are utilized to reduce the VIDEs to a system of algebraic equations. Applying the Floater-Hormann weights, the convergence analysis of the PBIFs method is studied. Finally, several numerical examples are provided to illustrate the efficiency and validity of the proposed method in acceptable computational times, and the results are compared with some existing numerical methods.

引用

页码：6030 / 6061

页数：32

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