A collocation method to find solutions of linear complex differential equations in circular domains

In this study, we introduce a collocation approach for solving high-order linear complex differential equations in circular domain. By using collocation points defined in a circular domain and Bessel functions of the first kind, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. Proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are given to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results obtained from the examples demonstrate the efficiency and accuracy of the present work. All of the numerical computations have been computed on computer using a code written in Matlab.