Abstract:
This thesis introduces a novel approach to solving Robin type singularly perturbed reaction
diffusion problems through cubic non-polynomial spline approximation on a piecewise mesh.
The methodology involves discretizing the solution domain using a piecewise mesh size, followed
by defining a cubic non-polynomial spline function and obtaining its derivatives. Subsequently,
the derivatives in the differential equations are transformed into difference approximations,
leading to a linear system of algebraic equations expressed in a three-term recurrence relation,
solvable through an elimination algorithm. The stability and consistency of the method are
thoroughly investigated to ensure its convergence. Furthermore, numerical model examples are
employed to validate the proposed method, with results compared against other methods cited in
the literature. The maximum absolute error and order of convergence for each model example
are presented to demonstrate the significant advancements offered by the present method.
