Abstract

A numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of operational matrices for this kind of equation is a cost-efficient scheme. Shifted Legendre polynomials are applied for solving Volterra integral equations with discontinuous kernels by converting the equation to a system of nonlinear algebraic equations. The convergence analysis is given for the approximated solution and numerical examples are demonstrated to denote the precision of the proposed method.

中文翻译：

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用运算矩阵法求解第一类不连续核非线性Volterra积分方程

摘要

提出了求解第一类具有不连续核的非线性Volterra积分方程的数值方法。对此类方程使用运算矩阵是一种经济高效的方案。平移勒让德多项式用于通过将方程转换为非线性代数方程组来求解具有不连续核的 Volterra 积分方程。对近似解进行了收敛分析，并通过数值算例说明了该方法的精度。