Finite integration method using chebyshev expansion for solving heat equation with non-local boundary conditions

Abstract

In this thesis, we devise numerical algorithms based on the finite integration method enhanced with Chebyshev polynomial expansion and also the Crank-Nicolson method to manipulate the spatial and temporal variables, respectively. These algorithms are designed to calculate approximate solutions for one-and two-dimensional heat equations that involve non-local boundary conditions, as well as for one-dimensional heat equations featuring Robin boundary conditions. Furthermore, we illustrate a selection of numerical examples to verify the efficiency and accuracy of the proposed algorithms by their analytical solutions.