High order WENO scheme for computational cosmology

This doctoral dissertation is concerned with the formulation and application of a high order accurate numerical algorithm suitable in solving complex multi dimensional equations and the application of this algorithm to a problem in Astrophysics.;The algorithm is designed with the aim of resolving solutions of partial differential equations with sharp fronts propagating with time. This high order accurate class of numerical technique is called a Weighted Essentially Non Oscillatory (WENO) method and is well suited for shock capturing in solving conservation laws. The numerical approximation method, in the algorithm, is coupled with high order time marching as well as integration techniques designed to reduce computational cost. This numerical algorithm is used in several applications in computational cosmology to help understand questions about certain physical phenomena which occurred during the formation and evolution of first generation stars.;The thesis is divided broadly in terms of the algorithm and its application to the different galactic processes. The first chapter deals with the astrophysical problem and offers an introduction to the numerical algorithm. In chapter 2 we outline the mathematical model and the various functions and parameters associated with the model. We also give a brief description of the relevant physical phenomena and the conservation laws associated with them.;In chapter 3, we give a detailed description of the higher order algorithm and its formulation. We also highlight the special techniques incorporated in the algorithm in order to make it more suitable for handling cases which are computationally intensive.;In the later chapters, 4-7, we explore in detail the physical processes and the different applications of our numerical scheme. We calculate different results such as the time scale of a temperature coupling mechanism, radiation and intensity changes etc. Different tests are also performed to illustrate the stability and accuracy of this algorithm. Chapter 8 is concerned with ongoing work and the future research that will be carried out in this topic.