## Numerical simulation of a singularly perturbed heat equation using the galerkin finite element method

 dc.contributor.author Fundi, Aweza dc.date.accessioned 2020-04-20T12:07:32Z dc.date.available 2020-04-20T12:07:32Z dc.date.issued 2016 dc.description Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF RA643.86.063) en_US dc.description.abstract Parabolic Partial differential equations play a crucial role in a large and varied range of disciplines in science and engineering. It is difficult to solve PDEs analytically; therefore a suitable numerical method is needed to solve them, such as the finite element method (FEM). In this research a linear singularly perturbed heat equation with an external heat source is solved numerically using the finite element method. Discretization of the spatial derivative is done using Galerkin Finite element discretization giving a semi-discrete system of Ordinary differential equations (ODEs). The resulting system of ODEs is integrated numerically using a Backward Euler schemes to obtain the numerical solution. Finally, some numerical simulations are carried out at different perturbation values to show how the solutions behave and also the effect of external heat source is analysed quantitatively. The results of the numerical solution of the singularly perturbed heat equation show that as the perturbation parameter decreases, a boundary layer forms at one end of the rod. Also the results show that after introduction of external heat source to the system, the heat source cause the temperature of the system to be higher than before addition of external heat source. en_US dc.identifier.citation Fundi, A. (2016) Numerical simulation of a singularly perturbed heat equation using the galerkin finite element method, Master dissertation, University of Dar es Salaam, Dar es Salaam en_US dc.identifier.uri http://41.86.178.5:8080/xmlui/handle/123456789/9629 dc.language.iso en en_US dc.publisher University of Dar es Salaam en_US dc.subject AIDS ( Disease) en_US dc.subject Transmission en_US dc.subject Alcoholism en_US dc.subject Mathematical models en_US dc.title Numerical simulation of a singularly perturbed heat equation using the galerkin finite element method en_US dc.type Thesis en_US
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