Application of non-polynomial SPLAGE algorithm for the numerical solution of singular two point boundary value problems using non-uniform mesh scheme

The purpose of this article is to present non-polynomial spline approximations using non-uniform mesh for the numerical treatment of singular boundary value problems. The numerical method is compact and exhibit homogeneous fourth order of convergence. The resulting nonlinear difference schemes are solved by alternating group explicit parallel algorithm. The utility of new schemes are illustrated by Burger’s equation, Duffing equation and Thomas Fermi model. Computational order of convergence and maximum absolute errors are given to demonstrate the efficiency of the non-uniform mesh approach.