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# Numerical solutions and simulation of parabolic partial differential equations

 dc.creator Mushumbusi, Philbert dc.date 2019-09-02T07:53:45Z dc.date 2019-09-02T07:53:45Z dc.date 2014 dc.date.accessioned 2019-12-06T12:20:31Z dc.date.available 2019-12-06T12:20:31Z dc.identifier Mushumbusi, P. (2014). Numerical solutions and simulation of parabolic partial differential equations (Master's dissertation). The University of Dodoma, Dodoma. dc.identifier http://hdl.handle.net/123456789/1355 dc.identifier.uri http://hdl.handle.net/123456789/16500 dc.description Dissertation (MA Mathematics) dc.description This dissertation is a study of finite difference numerical methods that are based on the principle of discretization. In chapter one presents the general overview of partial differential equations, Initial boundary value problems and derivations of Finite difference methods for one dimensional heat equation. A brief discussion of the truncation error is also presented. The second chapter is concerned with consistency, stability and convergence of the finite difference schemes for one dimensional and two dimensional parabolic partial differential equations. Two method of stability analysis, Fourier series method and Matrix Analysis method are used to analyze the stability of Crank-Nicolson and Alternating Direction Implicit (ADI) methods. Chapter three is devoted to numerical simulation of two dimensional parabolic equations. Two finite difference schemes, namely, Crank-Nicolson and Alternating Direction Implicit (ADI) methods are applied to the numerical solution of a two dimensional parabolic partial differential equation. Two Matlab routines one for Crank-Nicolson Scheme and another for ADI Scheme and dynamic pictures are included. dc.language en dc.publisher The University of Dodoma dc.subject Finite difference dc.subject Differential equations dc.subject Derivations dc.subject Boundary value dc.subject Heat equation dc.subject Simulation dc.subject Numerical solutions dc.subject Matrix Analysis dc.subject Fourier series dc.subject Matlab dc.subject Crank-Nicolson Scheme dc.title Numerical solutions and simulation of parabolic partial differential equations dc.type Dissertation
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