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Numerical simulation of finite-time blow-up in nonlinear ODEs, reaction-diffusion equations and VIDEs

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dc.contributor.advisor Dr. M. Khumalo; Prof. H. Brunner en_US
dc.contributor.author Dlamini, Phumlani Goodwill
dc.date.accessioned 2012-11-02T18:50:08Z
dc.date.available 2012-11-02T18:50:08Z
dc.date.issued 2012-11-02
dc.date.submitted 2012-02
dc.identifier.uri http://hdl.handle.net/10210/8054
dc.description M.Sc. en_US
dc.description.abstract There have been an extensive study on solutions of differential equations modeling physical phenomena that blows up in finite time. The blow-up time often represents an important change in the properties of such models and hence it is very important to compute it as accurate as possible. In this work, an adaptive in time numerical method for computing blow-up solutions for nonlinear ODEs is introduced. The method is named implicit midpoint-implicit Euler method (IMIE) and is based on the implicit Euler and the implicit midpoint method. The method is used to compute blow-up time for different examples of ODEs, PDEs and VIDEs. The PDEs studied are reaction-diffusion equations whereby the method of lines is first used to discretize the equation in space to obtain a system of ODEs. Quadrature rules are used to approximate the integral in the VIDE to get a system of ODEs. The IMIE method is then used then to solve the system of ODEs. The results are compared to results obtained by the PECEIE method and Matlab solvers ode45 and ode15s. The results show that the IMIE method gives better results than the PECE-IE and ode15s and compares quite remarkably with the 4th order ode45 yet it is of order 1 with order 2 superconvergence at the mesh points. en_US
dc.language.iso en en_US
dc.subject Midpoint-implicit Euler method en_US
dc.subject Differential equations, nonlinear en_US
dc.title Numerical simulation of finite-time blow-up in nonlinear ODEs, reaction-diffusion equations and VIDEs en_US
dc.type Thesis en_US

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