Numerical Solution of a Class of Nonlinear System of Second-Order Boundary-Value Problems: a Fourth-Order Cubic Spline Approach

Abstract

A cubic B-spline collocation approach is described and presented for the numerical solution of an extended system of linear and nonlinear second-order boundary-value problems. The system, whether regular or singularly perturbed, is tackled using a spline collocation approach constructed over uniform or non-uniform meshes. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order. The efficiency and applicability of the technique are demonstrated by applying the scheme to a number of linear and nonlinear examples. The numerical solutions are contrasted with both analytical and other existing numerical solutions that exist in the literature. The numerical results demonstrate that this method is superior as it yields more accurate solutions.

Keywords:

• collocation method
• finite element method
• boundary value problem
• differential equation

AMS Subject Classification:

• 30C45
• 31B30