On the Introduction of an Upwind Differencing into a Numerical Technique to Solve Boundary Value Problems (BVP)

Abstract

In practices, mathematical modelling problems can be expressed in the form of BVPs that arise frequently and majorly in the fields of science and engineering, such as electric circuits, fluid dynamics, the motion of rockets or satellites, and other areas of engineering applications. The study of Mildly Non-Linear Boundary Value Problems (MNBVP) is gaining popularity on daily bases as a result of several real-life practical models that degenerate into MNBVP. In recent time, several authors have formulate done numerical techniques or the other to determine the solutions of Boundary Value Problems (BVP); many of these techniques have not been able to easily solve Mildly Non-Linear Boundary Value Problems (MNBVP) because of its peculiarity. The MNBVP are problems that cannot be pinned as linear nor exclusively nonlinear rather; the function and it’s derivative are not all constants. This paper discusses the process of using the Upwind Differencing to reduce the BVP into tridiagonal system after which the Newton-Lieberstein method is employed to solve the mildly non-linear system so formed from the BVP. This imbedded technique requires dual independent processes that involve different Methods. The technique was employed to solve some problems with numerical results showing its flexibility, robustness, and efficiency of the technique. The results compare favourably with exact or analytical results.