Laguerre collocation method for the solution of linear complex differential equations in rectangular domains

In this study, a collocation method is presented for the approximate solution of high-order linear complex differential equations in rectangular domain. The method is based on Laguerre polynomials. By using Laguerre polynomials, matrix relations and collocation points in rectangular domain, complex differential equation problem is transformed to a system of linear algebraic equations. By solving this system, coefficients of the approximate solution are obtained. Also, rezidual error estimation technique is presented and the approximate solutions are improved by estimation error function. To explain the method, error estimation and rezidual improvement, numerical examples are given. The obtained results are compared with results of other methods.