Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method

Abstract

The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible—of course, this is supported by the competing Runge–Kutta method, among others, and reported through comparison plots and tables.

Keywords

• ODEs
• nonlinear ODEs
• IVPs
• BVPs
• ADM
• shooting method