High performance of the Remez algorithm in finding polynomial approximations for the solution of integral equations

In this paper, the solution of the general integral equation of the second kind is approximated using polynomials. These polynomials are obtained based on the Remez algorithm and the minimization of residual function. The nature of the use of the Remez algorithm in the proposed method will lead to the conversion of the integral equation to a system of algebraic equations and obtaining the best polynomial approximation for the solution of an integral equation.  Also, the convergence analysis of the approach is discussed. Finally, some numerical examples and comparisons with previous results confirm the efficiency and high accuracy of the presented method.

کلیدواژه ها:

Nonlinear integral equations ، Remez algorithm ، Best polynomial approximation ، Residual function ، Minimization ، Infinity norm