Solving Fredholm Integral Equations with Bernstein Multi-Scaling Functions

S Davaei far, Yadollah Ordokhani
2013 Zenodo  
In this article, efficient numerical methods for finding solution of linear and nonlinear Fredholm integral equations of the second kind based on Bernstein multi scaling functions are presented. Initially, the properties of these functions, which are a combination of blockpulse functions on [0,1) , and Bernstein polynomials with the dual operational matrix are presented. Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation which is
more » ... compatible to an algebraic equations system. The imperative of the Bernstein multi scaling functions for proper quantitative values of m and k, have a high accuracy and specifically the relative errors of the numerical solutions will be minimum. The presented methods from the computational viewpoint are very simple and attractive and the numerical examples at the end show the efficiency and accuracy of these methods.
doi:10.5281/zenodo.3470208 fatcat:ra3flw52ajbczhrdqwm76i3tvi