Finite Difference Method Applicable to Non-Linear Ordinary Differential Equations

Abstract

The key motive behind this work was to observe the precision of findings of finite difference method (FDM) of the system of non-linear second order ordinary differential equations (ODEs). This dissertation has two parts. In the first part, by applying the adequate similarity transformation the governing partial differential equations reduces to ordinary differential eqautions (ODEs). Then the solution of resulting ordinary differential equations acquires through finite difference method (FDM) and comparisn is made with the outcomes received from MATLAB’s built-in function bvp4c to assess the accuracy. Presented the impact of different parameters through graphs. Comparison of findings with the literature is done, and our findings are in favorable agreement. In second part, we considered nonlinear ordinary differential equations (ODEs) from fluid mechanics. Conversion of continuous nonlinear coupled ordinary differential equations into discrete differences equations aligned boundary conditions is made and solved in MATLAB. To validate our results, the coupled ordinary differential equations are also solved with MATLAB builtin function bvp4c. And we are in agreement with the already published research articles.