Efficient method for solution of nonlinear heat conduction problems

An efficient computer implementation of the heat conduction problem, with the associated initial and boundary conditions, is presented. The equation is discretized in the space domain using the Galerkin method, and the modified Crank-Nicolson midpoint rule is then applied, leading to a two-point recurrence scheme for the nodal temperatures. The application of this scheme to nonlinear problems is accomplished by using reference arrays, and subsequently multiplying them by time-dependent functions to account for the nonlinearities. The use of a reference value for the effective coefficient matrix is examined which avoids repeated factorizations. The flow-chart of this solution is presented and several examples using this method are solved.