HYBRID LAPLACE TRANSFORM FINITE-DIFFERENCE METHOD FOR TRANSIENT HEAT-CONDUCTION PROBLEMS

The new method involving the combined use of the Laplace transform and the finite difference method is applicable to the problem of time-dependent heat flow systems. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite difference method. The transformed temperature is inverted numerically by the method of Honig and Hirdes to obtain the result in the physical quantities. The present results are compared in tables with exact solutions and those obtained from the combined use of the Laplace transform and the finite element method. It is found that the present method is reliable and efficient.