A fitted mesh cubic spline in tension method for singularly perturbed problems with two parameters (Q2119865)

Summary: A numerical treatment via a difference scheme constructed by the Crank-Nicolson scheme for the time derivative and cubic spline in tension for the spatial derivatives on a layer resolving nonuniform Bakhvalov-type mesh for a singularly perturbed unsteady-state initial-boundary-value problem with two small parameters is presented. Error analysis of the constructed scheme is discussed and shown to be parameter-uniformly convergent with second-order convergence. Numerical experimentation is taken to confirm the theoretical findings.