Uniformly convergent extended cubic B-spline collocation method for two parameters singularly perturbed time-delayed convection-diffusion problems

Abstract

Abstract This work proposes a uniformly convergent numerical scheme to solve singularly perturbed parabolic problems of large time delay with two small parameters. The approach uses implicit Euler and the exponentially fitted extended cubic B-spline for time and space derivatives respectively. Extended cubic B-splines have advantages over classical B-splines. This is because for a given value of the free parameter $$ \lambda $$ λ the solution obtained by the extended B-spline is better than the solution obtained by the classical B-spline. To confirm the correspondence of the numerical methods with the theoretical results, numerical examples are presented. The present numerical technique converges uniformly, leading to the current study of being more efficient.

Keywords

• Singular perturbations
• Two parameter convection-diffusion problem
• Time delay
• Exponentially fitted method
• Extended cubic B-spline
• Boundary layer