Numerical Scheme for Two Parameter Singularly Perturbed Time-Delay Differential Difference Equations
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In this article, we treat two-parameter singularly perturbed differential difference equations with delay in the temporal variable. We develop a scheme using the backward Euler method on a uniform mesh for the discretization of the time derivative, while the spatial derivatives are discretized using a fitted operator finite difference approach on a uniform mesh. To improve the order of convergence, we apply the Richardson extrapolation technique. The convergence of the proposed scheme is analyzed, and found to be second-order convergent in both spatial and temporal variables. We conduct numerical experiments, and the outcomes are in agreement with the theoretical findings. We compare our approach to known approaches and discover that the present approach yields a more accurate approximate solution.
Abstract
In this article, we treat two-parameter singularly perturbed differential difference equations with delay in the temporal variable. We develop a scheme using the backward Euler method on a uniform mesh for the discretization of the time derivative, while the spatial derivatives are discretized using a fitted operator finite difference approach on a uniform mesh. To improve the order of convergence, we apply the Richardson extrapolation technique. The convergence of the proposed scheme is analyzed, and found to be second-order convergent in both spatial and temporal variables. We conduct numerical experiments, and the outcomes are in agreement with the theoretical findings. We compare our approach to known approaches and discover that the present approach yields a more accurate approximate solution.