# Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy

@article{Kadalbajoo2007NumericalMO, title={Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy}, author={Mohan K. Kadalbajoo and V. P. Ramesh}, journal={Appl. Math. Comput.}, year={2007}, volume={188}, pages={1816-1831} }

## 31 Citations

### Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay

- Mathematics
- 2020

### Numerical algorithm for singularly perturbed delay differential equations with layer and oscillatory behavior

- MathematicsNeural Parallel Sci. Comput.
- 2011

A new algorithm is presented to interpolate/exptrapolate the retarded term in terms of its neighbouring points and it is shown that the shift has significant effect on the behavior of the solution.

### Robust mid-point upwind scheme for singularly perturbed delay differential equations

- MathematicsComputational and Applied Mathematics
- 2021

This paper formulated the uniform converges of the scheme and considers singularly perturbed differential equations having delay on the convection and reaction terms, which converges uniformly with linear order of convergence.

### Uniformly Convergent Hybrid Numerical Method for Singularly Perturbed Delay Convection-Diffusion Problems

- MathematicsInternational Journal of Differential Equations
- 2021

This paper deals with numerical treatment of nonstationary singularly perturbed delay convection-diffusion problems. The solution of the considered problem exhibits boundary layer on the right side…

### Higher Order Uniformly Convergent Numerical Algorithm for Time-Dependent Singularly Perturbed Differential-Difference Equations

- MathematicsDifferential Equations and Dynamical Systems
- 2019

This paper presents a higher order uniformly convergent discretization for second order singularly perturbed parabolic differential equation with delay and advance terms. The retarded terms are…

### Upwind and midpoint upwind difference methods for time-dependent differential difference equations with layer behavior

- MathematicsAppl. Math. Comput.
- 2008

### Numerical method for a singularly perturbed convection-diffusion problem with delay

- MathematicsAppl. Math. Comput.
- 2010

### Exponentially fitted tension spline method for singularly perturbed differential difference equations

- Mathematics
- 2021

In this paper, singularly perturbed differential difference equations having delay and advance in the reaction terms are considered. The highest order derivative term of the equation is multipliedby…

### Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid

- Computer Science, Mathematics
- 2011

A matrix methods is presented for approximate solution of the second-order singularly-perturbed delay differential equations, which reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem.

### An a Priori Harmonic Mesh for Singularly Perturbed Boundary Value Problems

- MathematicsInternational Journal of Applied and Computational Mathematics
- 2018

In this article, we present a harmonic series (partial sum) based a priori mesh denoted by $$H(\ell )$$H(ℓ) having both computational advantages and improved accuracy when compared with generalized…

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