An Efficient Numerical Method for a Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the proposed method.

Keywords:

Collocation method , shifted Jacobi polynomial , Singular boundary value problem , Exponential nonlinearity , Product nonlinearity