A Fourth-Order Compact Finite Difference Scheme for First Order Initial Value Problems
Abstract
In this paper, a fourth order Compact Finite Difference Scheme(CFD) for the numerical solution of first order initial value problems (IVPs) of Ordinary Differential Equations (ODEs) is discussed. Compact finite difference scheme is a class of numerical methods that are particularly designed for solving Partial Differential Equations (PDEs). However, in this paper, we consider the compact finite difference scheme for approximating the numerical solution of ordinary differential equations. The application of this scheme enables the solution of first-order ODEs across all grid points in just one computational sweep (single iteration), rather than requiring repeated iterative updates. Numerical examples have been included to demonstrate the accuracy of the scheme and Numerical results compared with the exact solution and other existing methods from recent literature. The scheme is shown to be efficient for the numerical integration of first order differential equations.
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