Efficient numerical methods for solving nonlinear high-order boundary value problems

Abstract

Nonlinear problems are prevalent in plasma physics, solid state physics, fluid dynamics, chemical kinetics, structural and continuum mechanics and there is high demand for computational tools to solve these problems. In this paper, we have developed two methods, namely, Embedded Perturbed Chebyshev Integral Collocation Method and Embedded Perturbed Bernstein Integral Collocation Method for the efficient numerical solution of nonlinear high-order boundary value problems. Newton-Raphson-Kantorovich linearization scheme of appropriate orders are employed to linearize the nonlinear equations and then resorting to iterative procedure. Numerical results are included to demonstrate the reliability and efficiency of the methods. Comparison between exact and approximate solutions is made and our proposed methods compared favourably with known numerical methods used in solving the same nonlinear problems considered.