Numerical Solutions To Partial Differential Equations - Finite Difference Approach

ABSTRACT

This dissertation contains materials on numerical solutions to partial differential equations only appropriate for senior level undergraduate. The reader based on this dissertation should have had introductory courses in Calculus, linear algebra and general numerical analysis. A formal course in ordinary or partial differential equations would be useful. In our study, it should be understood that, there are many procedures that come under the name numerical methods. We shall see how the very popular finite difference methods can be used to solve elliptic equations, hyperbolic equations and parabolic equations. To begin, we introduce the idea of numerical methods. We then show how to use these finite differences methods to solve the heat problems, wave problems, Laplace equations and Poisson equations. Moreover, systems of algebraic equations have been solved numerically by using Gauss elimination methods and substitution methods. Also the reader will find how numerical solutions to partial differential equations are applicable in daily life experience.