A nonasymptotic method for general linear singular perturbation problems
Journal of Optimization Theory and Applications
On numerical integration of a class of singular perturbation problems
Journal of Optimization Theory and Applications
SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
A Taylor polynomial approach for solving differential-difference equations
Journal of Computational and Applied Mathematics
A Taylor polynomial approach for solving differential-difference equations
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Hi-index | 0.00 |
In this paper, we use a numerical method to solve boundary-value problems for a singularly-perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Similar boundary-value problems are associated with expected first exit time problems of the membrane potential in models for the neuron. The stability and convergence analysis of the method is given. The effect of a small shift on the boundary-layer solution is shown via numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method.