Numerical Modelling of Application of Higher Order Accurate and Compact Numerical Scheme

Bridging the Gap: Numerical Approximation of Differential Equations

Abstract

Differential equations (PDEODEs) form the basis of many mathematical models of physical, chemical and biological phenomena, and more recently their use has spread into economics, financial forecasting, image processing and other fields. It is not easy to get analytical solution treatment of these equations, so, to investigate the predictions of PDE models of such phenomena it is often necessary to approximate their solution numerically. In most cases, the approximate solution is represented by functional values at certain discrete points (grid points or mesh points). There seems a bridge between the derivatives in the PDE and the functional values at the grid points. The numerical technique is such a bridge, and the corresponding approximate solution is termed the numerical solution.