NUMERICAL SOLUTIONS OF PARABOLIC DIFFERENTIAL EQUATIONS:FINITE DIFFERENCE METHOD

Abstract

This Thesis presents Numerical solutions of Parabolic differential equations finite difference method. Parabolic differential equation of second order was studied using FDM . In this Thesis ,we discussed basic things of these methods. Secondly ,we studied boundary conditions involving derivatives and obtain finite difference formulas by using forward, back ward and central difference formulas approximating PDE of boundary value problems. The last section devoted to determining an approximate solution for boundary value problems .To identify the efficient of the three methods explicit, implicit and Crank Nicolson methods were discussed. The advantage and disadvantage of the three methods were explained briefly. The stability of these methods were shown by using Fourier method and Matrix method by using Mat-lab. Additionally Sketch pad software were usedto draw tables and different sketches. The error between the Numerical solution obtained by formulas and the numerical solutions by soft ware were analyzed.