COMPUTATIONAL STUDY OF SOME NUMERICAL TECHNIQUES FOR SOLVING BOTH TIME DEPENDENT AND INDEPENDENT partial DIFFERENTIAL EQUATIONS PDEs

Abstract

The thesis begins with Chapter-I which gives introduction to numerical PDEs, their basic concept and solution. We provide a discussion on time independent PDEs: Laplace equation and time dependent PDEs: heat equation and wave equation. Furthermore, the objectives of the research work for this thesis are presented in this chapter. newlineIn Chapter-II we have carried out a review of literature for the different numerical schemes, namely: finite difference method (FDM), finite element method (FEM) and finite volume method (FVM), adopted to study partial differential equations. newlineIn Chapter-III a few more important theoretical aspects for designing a numerical scheme, such as initial and boundary conditions for PDEs in general is discussed. Moreover some more numerical methods other than the FDM, FVM and FEM namely, finite point-set method, spectral method, boundary integral method, mesh-less or mesh-free method and gradient discretization method are also elucidated in this chapter. We also discuss a few mo newline