A Method of Solution for the One-Dimensional Heat Equation Subject to Nonlocal Conditions

Abstract

The problem of solving the one-dimensional heat equation ∂φ/∂t - ∂²φ/∂x² = f(x, t) subject to given initial and nonlocal conditions is considered. It is solved in the Laplace transform domain by taking the Laplace transform of the unknown function φ with respect to time t. The physical solution is recovered with the help of a numerical technique for inverting the Laplace transform.