Fibonacci wavelet based numerical method for the solution of nonlinear Stratonovich Volterra integral equations

Abstract

This article provides an effective technique to solve nonlinear Stratonovich Volterra integral equations (NSVIE). These equations can be reduced to a system of nonlinear algebraic equations with unknown Fibonacci coefficients, by using Fibonacci wavelets, their operational matrix of integration and stochastic operational matrix of integration and these equations can be solved by numerical methods such as Newton's method. Error estimate of the proposed method is given. Moreover, the results obtained by the method proposed are compared to block pulse functions and Legendre wavelets method with two numerical examples to show that the method described is precise and accurate.