A NUMERICAL METHOD FOR SOLUTION OF LINEAR TRANSIENT HEAT CONDUCTION EQUATIONS

Abstract

A new numerical integrating method is compared in this paper with the most popular two-level schemes, as the Crank-Nicolson (C.-N.), the Galerkin (G.), the EulerCauchy (E.-C.), the Backward Difference (B.-D.), and the 4th order Runge-Kutta (R-K.4). This procedure, the Weighting-Function Method (W.-F. M.) uses not a constant weighting factor (like 1/2 in C.-N. scheme) but a weighting function. The weighting function depends on the actual problem and on the time step. The approximating weighting function is calculated in the first few steps until it reaches a constant value; after that, the calculation will be continued using this constant weight. The W.-F. M. was tested on different simple examples, and was compared with the analytical solution and with the results of other schemes. The W.-F. M. has the best accuracy.