Abstract
A time dependent singularly perturbed differential-difference equation is considered. The problem involves time delay and general small space shift terms. Taylor series approximation is used to expand the space shift term. A robust numerical scheme based on the backward Euler scheme for the time and classical upwind scheme for space is proposed. The convergence analysis is carried out. It is observed that the proposed scheme converges almost first order up to a logarithm term and optimal first order in space on the Shishkin and Bakhvalov–Shishkin mesh, respectively. Numerical results confirm the efficiency of the proposed scheme, which are in agreement with the theoretical bounds.
References
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Articles in the same Issue
- Frontmatter
- L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative
- On tangential approximations of the solution set of set-valued inclusions
- Stabilization of the wave equation with a nonlinear delay term in the boundary conditions
- Fixed point to fixed circle and activation function in partial metric space
- A note on the validity of the Schrödinger approximation for the Helmholtz equation
- Certain classes of analytic functions defined by Hurwitz–Lerch zeta function
- A new factor theorem on absolute matrix summability method
- On a solution to a functional equation
- Hydromagnetic effects on non-Newtonian Hiemenz flow
- Stability of a class of entropies based on fractional calculus
- Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
- Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts
- Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control
- On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions
- Extended homogeneous balance conditions in the sub-equation method
Articles in the same Issue
- Frontmatter
- L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative
- On tangential approximations of the solution set of set-valued inclusions
- Stabilization of the wave equation with a nonlinear delay term in the boundary conditions
- Fixed point to fixed circle and activation function in partial metric space
- A note on the validity of the Schrödinger approximation for the Helmholtz equation
- Certain classes of analytic functions defined by Hurwitz–Lerch zeta function
- A new factor theorem on absolute matrix summability method
- On a solution to a functional equation
- Hydromagnetic effects on non-Newtonian Hiemenz flow
- Stability of a class of entropies based on fractional calculus
- Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
- Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts
- Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control
- On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions
- Extended homogeneous balance conditions in the sub-equation method