Characteristic mode solution of complex-coefficient complex-solution differential equations

Abstract

Computation of complex coefficient complex solution differential equations is a problem that arises in various domains of science and engineering, and has thus received much attention in years, with marked recent progress. This thesis aims at applying the Theory of Characteristic Mode (TCM) approach along with the Method of Moments (MoM) in solving these problems with emphasis on procedures for higher differential equations. Several available methods, known in literature, are available for solving the problem and their complexity differ based on the accuracy of the solution. The general method is presented and a simplified version of it is adopted to address this problem considering first, third, and forth orders complex-coefficients complex solution differential equations. These examples are considered to clarify the approach and present the simplicity of the method. As illustrated in this proposal, The approach can be introduced along with other methods, and can be considered as an attractive way to solve these special occurrences differential equations and other boundary value problems.