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Numerical solutions and simulation of parabolic partial differential equations

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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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