Abstract:
In this thesis, fourth-order finite difference scheme on non-uniform mesh for semilinear
singularly perturbed reaction-diffusion problem is presented. The quasilinearization technique is
used to linearize the semilinear term. It is formulated by discretization of the solution domain
and then replace the differential equation by finite difference approximation that gives the
system of algebraic equation. The method is shown to be fourth-order convergent. Further, it is
observed that the convergence is independent of the perturbation parameter. Numerical
illustrations are investigated on some examples to support the theoretical results and the
applicability of the method. Furthermore, the proposed method produces more accurate solution
than some existing methods in the literature.
