Efficient Numerical Approaches for Solving Singularly Perturbed Delay Differential Equations with Discontinuities and Integral Boundary Constraints
Abstract
This research focuses on studying a specific problem involving a second-order delay differential equation that has a discontinuous source term over the interval [0, 2] with an integral boundary condition. The discontinuity is expected to happen at a point \(d \in (0,2)\) , while a tiny positive parameter adjusts the leading coefficient. The solution displays boundary layers at \(x = 0\) and \(x = 2\) , and there may be interior layers at \(x = 1\) , \(x = d\) , and \(x = 1 + d\) , depending on the location of d . To tackle this issue, a finite difference method is implemented on a segmented Shishkin mesh. We establish first-order uniform convergence of the scheme with respect to the perturbation parameter, supported by numerical validation.
Fields of Study & Subjects
Differential Equations and Numerical Methods
Differential Equations and Boundary Problems
Numerical methods for differential equations
Publication details
- Journal / source
- Journal of Nonlinear Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 33
- Issue
- 1
- Publication date
- 20 February 2026
- Language
- EN