This project provides a practical overview of numerical solutions to parabolic partial differential equation in Chebyshev series. The method is given for the numerical solution of a linear parabolic equation in the form of a Chebyshev series. The equation is first transformed into a set of ordinary differential equation for the Chebyshev coefficients, and the numerical solution of these equations is obtained by numerical method.

A Thesis Submitted to Department of Mathematics Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics.