Trial solution methods to solve the hyperbolic heat conduction equation

Trial solution methods combined with Laplace transformation technique are u sed to present an analytic approximate solution for the hyperbolic heat con duction (HHC) equation. The trial solution methods used in this work are we ighted residual methods and Ritz variational method. The weighted residual methods involves the application of different optimizing criteria, which ar e the collocation, subdomain, least square and the Galrekin optimizing meth ods. Trial solution procedures are carried out after transforming the HHC e quation from the time domain into the Laplace domain. The solution of the t ransformed equation is expanded in the form of a shape function. The shape function is a function of space and undetermined coefficients. In this work , two shape functions are used: polynomial and hyperbolic. Applying the tri al solution methods yields a system of algebraic equations that is solved s ymbolically using a commercial computerized symbolic code. Finally, the sol ution in time domain is obtained by inverting the solution of the transform ed equation. It is found that the trial solution methods using polynomial approximate fu nctions up to fourth order are not able. to capture the sharp gradient in t he vicinity of the heat wave. Whereas; the hyperbolic shape function mimic the exact solution for all methods. (C) 2000 Elsevier Science Ltd.