Applications of framelets for solving third kind integral- integral equations

Abstract

This article is dedicated to obtain numerical solution for semi-explicit integral-algebraic equation of third kind (IAE). We used tight wavelet frames (framelets) to obtain the numerical solution. The framelets system generated by unitary extension principle and oblique extension principle based on the B-spline refinable function. We provide some numerical examples to show the efficiency of the proposed method.  The obtained numerical results of our method compared with those obtained from Spline and discretized colocation methods. We confirm that, our proposed method achieves accurate and efficient results than others.