Solving Higher Orders Linear Complex Partial Differential Equations via Two Dimensional Differential Transform Method

Abstract

Complex partial differential equation (CPDEs( appeared around the year 1900. D. Pompeiu was a famous mathematician who left a large impact in this field through introducing the Pompeiu integral operator, which forms a basis in the subject CDEs. The complexity of some real-world problems has been conquered via the methods of solution for CDEs . Two-dimensional differential transform was proposed in 1999 by Chen and Ho as a powerful tool for solving PDEs and . Many researchers used two dimensional differential transform method for solving linear complex partial derivative equations such as to solve linear CPDEs and for nonlinear CPDEs . This paper presents two-dimensional differential transform for the complex partial derivatives of higher orders for a complex functions of two complex independent variables, and then use these complex partial derivatives to find an exact solution to a complex partial differential equation of the fourth order using two-dimensional differential transform method.

Keywords

• complex differential equations,,
• ,،two dimensional differntial transform,,
• ,،partial differential equations