Numerical approximations based on sextic B-spline functions for solving fourth-order singular problems

Abstract

In this work, a new access for solving fourth-order singular boundary value problem (SBVP) by using sextic B-spline is presented. The SBVP yields in mathematical modelling of several real-world development essentially electro-hydrodynamics, chemical reactions, thermal explosions, fluid dynamics, aerodynamics and atomic nuclear reactions. It must be indicated that the original non-linear boundary value problem (BVP) is first remodelled into a linear BVP by quasilinearization technique. Convergence analysis of the method is explored. Three trial evidences are examined to determine the accuracy and suitability of the described technique and to validate the analytical results. The proposed method is simple, robust and straightforward for solving the non-linear SBVP.