Vietnam Journal of Mathematics

, Volume 44, Issue 1, pp 5–28

# Numerical Solution of a Non-Linear Volterra Integral Equation

• P. Torabi
• S. Sauter
Article

## Abstract

In this paper, a numerical method to solve non-linear integral equations based on a successive approximation technique is considered. A sequence of functions is produced which converges to the solution. The process includes a fixed point method, a quadrature rule, and an interpolation method. To find a total bound of the error, we investigate error bounds for each approximation and by combining them, we will derive an estimate for the total error. The accuracy and efficiency of the method is illustrated in some numerical examples.

## Keywords

Nonlinear quadratic Volterra integral equation Fixed point theorem Measure of noncompactness Fixed point method Adaptive quadrature Nonuniform interpolation nodes

## Mathematics Subject Classification (2010)

45D05 65D07 65R20

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