Approximate solution of complex differential equations for a rectangular domain with Taylor collocation method

Abstract

In this study, Taylor collocation method is investigated for the approximate computation of high-order linear complex differential equations. Using the collocation points on any rectangular domain in the complex plane, the method transforms the given complex differential equation and the mixed conditions to matrix equation with unknown Taylor coefficients. By means of the obtained matrix equations, the Taylor coefficients can be easily computed. Hence, the finite Taylor series approach is obtained. Also, examples are presented and the results are discussed.