Legendre waveler operational matrix method for solving systems of fractional differential equations.

Abstract

This thesis introduces a new numerical approach to solve high order and fractional order differential equations of the linear and non-linear forms and systems of such equations utilizing the Legendre wavelet operational matrix method. We first formulated the operational matrix and its fractional derivatives in some special conditions by using some significant features of Legendre wavelets and shifted Legendre polynomials. Then, the high order and fractional order differential equations and systems of such equations were transformed to a system of algebraic equations by using these operational matrices. At the end of each chapter of the thesis, the introduced tecnique is tested on several illustrative examples. Comparing the methodology with several recognized methods demonstrates that the most important advantages of the introduced method are the understandibility of the calculations and its accuracy.