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Abstract
In a previous paper a transform (spectral)-iterative method, with a new mode of iteration, was introduced for solving a variety of nonlinear problems including nonlinear (quadratic) or variable coefficient chemical reactions in planar catalyst pellets with reference to its possible application to other geometries. In this paper we further develop the method, with more general modifications of the iteration, and where we also use the Green's function for a nonlinear integral equation representation of the problem in the physical space. Such a representation offers a more direct way of involving general nonlinearities besides the quadratic one of the last paper. In addition, the modified iteration for both this (physical space) and the transform (spectral) representations can now be supported by a simple test or condition, that can explain its better convergence. The method is illustrated here for cylindrical and spherical pellets, with various relevant nonlinearities and, for reference most of these results are compared with those done by a well known method like the shooting method.