Decomposition methods for non-linear, non-characteristic Cauchy heat problems

Solutions for one-dimensional heat equations with a non-linear heat source, in the case where both the temperature and the heat flux are given at a single boundary, are obtained using variants of the Adomian decomposition method. The given quantities may be any infinitely differentiable functions satisfying certain conditions. The solutions are applicable for one-dimensional (radial) heat flow in slabs, cylinders and spheres.