A Method for the Approximate Solution of the Heat Equation

摘要

A method is presented for obtaining approximate analytical solutions to the heat equation. The procedure combines the Laplace transform and Galerkin techniques.nIt is applied first in this report to three problems for which exact, analytical solutions are available. Reasonably accuracte, approximate solutions are obtained to these problems without great computational effort.nThe combined Laplac -Galerkin method is then applied to a more complex problem for which an exact analytical solution is not avail¬able, involving heat flow in an angle.__For comparison purposes, a solution to the same problem was obt ined by electrical analogy methods. Good agreement between the two solutions is obtained in some portions of the angle, with larger discrepancies in others. It is concluded that for problems of this type and complexity, an accurate approximate solution using this method would require many arbitrary parameters and considerable computational effort.