A new exponential Jacobi pseudospectral method for solving high-order ordinary differential equations

This paper reports new orthogonal functions on the half line based on the definition of the classical Jacobi polynomials. We derive an operational matrix representation for the differentiation of exponential Jacobi functions which is used to create a new exponential Jacobi pseudospectral method based on the operational matrix of exponential Jacobi functions. This exponential Jacobi pseudospectral method is implemented to approximate solutions to high-order ordinary differential equations (ODEs) on semi-infinite intervals. The advantages of using the exponential Jacobi pseudospectral method over other techniques are discussed. Several numerical examples are presented to confirm the validity and applicability of the proposed method. Moreover, the obtained results are compared with those obtained using other techniques.