A Taylor collocation method for the numerical solution of complex differential equations with mixed conditions in elliptic domains

An approximate method for solving higher-order linear complex differential equations in the elliptic domains is proposed. The approach is based on a Taylor collocation method, which consists of the matrix representation of expressions in the differential equation and the collocation points defined in the elliptic domain. Illustrative examples are included to demonstrate the validity and applicability of the technique, and performed on the computer using a program written in Maple9.