An Improved Method for Solution of the Linear Diffusion Equation

Abstract

The diffusion equation is often solved numerically, using finite-difference techniques. The linear one-dimensional diffusion equation may also be solved by the method of variation of parameters, which yields a solution in the form of an infinite series of products of eigenfunctions and time-varying coefficients. The series form of solution has advantages over finite-difference techniques, but the rate of convergence is often not sufficient to yield useful results. This paper presents an alternative form of the series solution for one-dimensional, Cartesian, homogeneous, and temperature-independent property conditions. The methodology, which exhibits excellent convergence, is applicable to several related problems.