Abstract:
In this study we present the numerical solution o fboundary value problems for
the reaction-diffusion equations in 1-d and 2-d that model phenomena such as
kinetics and population dynamics.These differential equations are solved nu-
merically using the finite element method (FEM).The FEM was chosen due to
several desirable properties it possesses and the many advantages it has over
other numerical methods.Some of its advantages include its ability to handle
complex geometries very well and that it is built on well established Mathemat-
ical theory,and that this method solves a wider class of problems than most
numerical methods.The Lax-Milgram lemma will be used to prove the existence
and uniqueness of the finite element solutions.These solutions are compared
with the exact solutions,whenever they exist,in order to examine the accuracy
of this method.The adaptive finite element method will be used as a tool for
validating the accuracy of theFEM.The convergence of the FEM will be proven
only on the real line.
