A Convergent Finite Difference Scheme for a Class of Nonlinear Boundary Value Problems

Abstract

In this work, we concerned the approximations of solutions for a type of nonlinear second-order boundary value problems which are commonly encountered in applied mathematics and engineering practices. A finite difference method is used to discretize the governing equations, resulting in a system of nonlinear algebraic equations. Existence and uniqueness of the discretized solution are proved under rather mild restrictions. Furthermore, the proposed method is extensively analyzed theoretically, in which its consistent stability and convergent behaviors are mathematically proved. Some numerical examples are also presented to verify the theoretical results and demonstrate some computational efficiency.