Fitted cubic spline in tension difference scheme for two-parameter singularly perturbed delay parabolic partial differential equations

Abstract

A numerical study of a two-parameter singularly perturbed time-delay parabolic equation has been initiated. The proposed technique is based on a fitted operator finite difference scheme. The first step involves the discretization of the time variables using the Crank–Nicolson method. This results in singularly perturbed semi-discrete problems, which are further discretized in space using the exponentially fitted tension-spline finite difference method. The error analysis is carried out. It is shown to be parameter-uniformly convergent and second-order accurate. To support the theoretical results, numerical experiments are carried out by applying the proposed technique to two test examples.

Keywords

• Singular perturbations
• Two parameters
• Delay parabolic differential equation
• Cubic spline in tension
• Fitted operator
• Boundary layer