Transient heat flow analysis using the fundamental collocation method

The fundamental collocation method for general two dimensional transient heat flow problems in solids is presented. The numerical procedure is applied directly to heat conduction in the time domain and is illustrated using several example problems. The method is capable of handling problems of arbitrary shapes subjected to arbitrary initial conditions and mixed time-dependent boundary conditions. Its simplicity and minimal computational effort combined with accuracy and stability of the results make the method an excellent alternate approach to domain methods such as the finite difference and finite element methods.