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

Subject Areas : International Journal of Industrial Mathematics

M. Maleki Miyane ¹ , S. Abbasbandy ²

1 - Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran
2 - Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran

Received: 2016-08-06 Accepted : 2016-08-07 Published : 2019-01-01

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

Abstract :

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.