Numerical solution of two dimensional heat equations inpolar coordinates system using crnk-nicolson with hockney’s method.

Abstract

In this thesis, Crank-Nicolson with Hockney's method is presented for solving Two dimensional Heat equation in polar coordinates system. First the given partial differential equation of two dimensional heat equation in polar coordinates system is converted into equivalent linear equation using Crank-Nicolson approximation .By extending Hockney's method the linear equation is reduced in to main and sub diagonal system which can be solved using Thomas algorithm. To validate the applicability of the proposed method two model examples with exact solution have been solved. The result presented in tables show that Crank-Nicolson with Hockney's method is faster than Crank-Nicolson method in computational time.