A monotonicity procedure for the accurate, efficient solution of certain heat-transfer problems with variable thermal properties

An efficient solution procedure of high accuracy is described for the numerical solution of nonlinear boundary value problems associated with heat-transfer and reaction-diffusion processes. Constructive existence-uniqueness theorems lead to Newton/Picard iterative schemes for bounding the positive solutions of these problems. The iteration schemes are discretised as matrix tridiagonal systems of error order O(h2). Richardson extrapolation can be exploited to produce very accurate results; comparisons are made with the results of other methods on specific examples.