A Laplace transform-based fundamental collocation method for two-dimensional transient heat flow

The fundamental collocation method (FCM) is extended to handle two dimensional transient heat conduction problems in solids. The method is applied in the Laplace transform domain, after which an inversion technique is used to retrieve the time-domain solution. Examples are used to illustrate the method and a technique for evaluating accuracy is discussed. The performance was found to be very good. The method is capable of handling regions of arbitrary shapes, subjected to constant temperature initial conditions and mixed type, time-independent boundary conditions. Due to its inherent advantages over the domain-oriented techniques like the finite element and, finite difference methods, the Laplace transform-based FCM approach presented here may be regarded as a simpler method for solving a wide variety of time-dependent problems in heat conduction and related fields.