Özet:
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.
