| In this dissertation, we have extended the method of Generalized Quasilinearization to reaction diffusion systems. We combine the method of coupled lower upper solutions and the Generalized Quasilinearization method to prove the existence of solution of the reaction diffusion systems, when the forcing functions are the sum of the convex and concave functions. These results are improvement over the known results in the scalar case of reaction diffusion equations. We demonstrate the applications of the theoretical results with numerical examples. We also present numerical examples for the scalar cases as well. Finally, we develop a monotone iterative technique to prove the existence of coupled weak extremal solutions of the semilinear elliptic systems. We also prove the existence of the unique solution for the semilinear elliptic systems under suitable conditions. |
