Fitted mesh methods based on non-polynomial splines for singularly perturbed boundary value problems with mixed shifts

Abstract

In this paper, numerical schemes based on non-polynomial splines, namely, spline in compression, tension, and adaptive spline, are constructed for singularly perturbed boundary value problems with mixed shifts. A convergence analysis is carried out on the proposed methods. A comparitive study of the results is performed on test problems and presented in the form of tables. Graphs are drawn to illustrate the behavior of the solution to the problems.

Keywords

• singular perturbations
• delay
• differential equations
• numerical methods
• fitted mesh
• splines