A Robust computational method for singularly perturbed delay parabolic convection-diffusion equations arising in the modeling of neuronal variability

Document Type : Research Paper


1 Department of Mathematics, Wollega University, Nekemte, Ethiopia.

2 Department of Mathematics, Jimma University, Jimma, Ethiopia.


‎In this study‎, ‎a robust computational method involving exponential cubic spline for solving singularly perturbed parabolic convection-diffusion equations arising in the modeling of neuronal variability has been presented‎. ‎Some numerical examples are considered to validate the theoretical findings‎. ‎The proposed scheme is shown to be an $\varepsilon-$uniformly convergent accuracy of order $ O\left( \left( \Delta t\right)‎ +‎h^2 \right) $‎.


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