Gerald Tendayi Marewo

By Stanford Shateyi, Fazle Mabood and Gerald Tendayi Marewo

The problem of MHD micropolar fluid, heat and mass transfer over unsteady stretching sheet through porous medium in the presence of a heat source/sink and chemical reaction is presented in this chapter. By applying suitable similarity transformations, we transform the governing partial differential equations into a system of ordinary differential equations. We then apply the recently developed numerical technique known as the Spectral Quasi-Linearization Method. The validity of the accuracy of the technique is checked against the bvp4c routine method. Numerical results for the surface shear stresses, Nusselt number and the Sherwood number are presented in tabular form. Also numerical results for the velocity, temperature and concentration distribution are presented in graphical forms, illustrating the effects of varying values of different parameters.

Part of the book: Numerical Simulation

By Gerald Tendayi Marewo

In this chapter, we present a modified version of the spectral relaxation method for solving singular initial value problems for some Emden-Fowler equations. This study was motivated by the several applications that these equations have in Science. The first step of the method of solution makes use of linearisation to solve the model problem on a small subinterval of the problem domain. This subinterval contains a singularity at the initial instant. The first step is combined with using the spectral relaxation method to recursively solve the model problem on the rest of the problem domain. We make use of examples to demonstrate that the method is reliable, accurate and computationally efficient. The numerical solutions that are obtained in this chapter are in good agreement with other solutions in the literature.

Part of the book: Recent Advances in Numerical Simulations