Al-Ofl, Abdalaziz Saleem (2008) Analysis of complex nonlinear reaction-diffusion equations. Doctoral thesis, Durham University.
A mathematical analysis has been carried out for some nonlinear reaction- diffusion equations on open bounded convex domains Ω C R(^d)(d < 3) with Robin boundary conditions- Existence, uniqueness and continuous dependence on initial data of weak and strong solutions are proved. A numerical analysis has also been undertaken for these nonlinear reaction- diffusion equations on the above domains. A fully practical piecewise linear finite element approximation is proposed for which existence and uniqueness of the numerical solution are proved. Semi-discrete and fully discrete error estimates are given. A practical algorithm for computing the numerical solution is given and its convergence is proved. Finally, some numerical simulations in one-dimensional space are exhibited.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||08 Sep 2011 18:31|