Solution of differential equations using differential quadrature method

This thesis presents one of the numerical discretization technique which is known as Differential Quadrature Method (DQM). In this thesis, linear ordinary and linear partial differential equation problems were solved by using DQM. In addition to DQM, Finite Difference Method (FDM) was also investigated for comparing DQM and FDM with each other. This thesis consists of seven chapters. First chapter is named as introduction. In the second chapter, mathematical fundamentals of DQM, which are linear vector space analysis and function approximation, were given. Third chapter gives information about Polynomial-based Differential Quadrature Method (PDQM). In the fourth chapter, PDQM was applied to linear ordinary differential equations and approximate solutions obtained were compared with the exact solutions. In the fifth chapter the relationship between PDQM and FDM were discussed. In the sixth chapter, PDQM was applied to linear partial differential equations and approximate solutions obtained were compared with the exact solutions. Finally, in the seventh chapter results obtained were discussed.