Semi-Analytical Solution of Volterra Integral Equation by DTM and RDTM رسالة ماجستير

Abstract

The differential transform method (DTM) and the reduced differential transform method (RDTM) are semi-analytical numerical methods which can be applied to various kinds of ordinary and partial differential equations besides several types of integral equations. In this work, the theory of DTM and RDTM of one and two-dimensional Volterra Integral Equation (VIE) have been introduced. The solution of three- dimensional VIE has been investigated. In addition, we have proved some additional theorems related to this type of integral equations. Furthermore, the theory of three dimensional DTM has been successfully extended to three dimensional RDTM. Finally, a comparison between the two methods has been carried and to show the advantage of RDTM over DTM in solving three dimensional VIE.