Solution of some partial differential equations using finite difference method

Abstract

Mathematical models arises not only in applied mathematics but also in engineering, medical, finance, computers, physics, chemistry, etc. These models shape up as ordinary or partial differential equations, linear or non-linear in nature. In comparison to ordinary differential equations, partial differential equations are difficult to handle. Some are even difficult to be solved for the exact solution. In such instances, the idea to implement a numerical method is to find the approximate solution of the real life problem. newline newlineFinite difference method -FDM- is one among the numerical methods, which is easy to implement, sufficiently accurate and versatile in nature. These features makes FDM an evergreen method with wide application to solve numerous practical problems. According to the needs, certain modifications have being carried out in the standard FDM to enhance its applicability. Compact finite difference method is one such extension of standard FDM, which is comparatively more accurate with higher-order of convergence. The present work deals mainly with sixth-order compact finite difference method to solve the linear and non-linear partial differential equations. newline newline