The precise integration method for semi-discretized equation in the dual reciprocity method to solve three-dimensional transient heat conduction problems

A dual reciprocity precise integration method (DRPIM) is presented to solve 3-dimensional transient heat conduction problems. In the presented method, the transient heat conduction problem, which is an initial boundary value problem, is transformed into an initial value problem (IVP) through a dual reciprocity scheme. Then an analytical solution, which is described by terms of the matrix exponential function (MEF), to this IVP is applied. A precise integration method (PIM) is finally applied to compute the MEF accurately. The accuracy and stability of the presented method are demonstrated by three numerical examples.