Hybrid Algorithm for Singularly Perturbed Delay Parabolic Partial Differential Equations
This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify the theoretical investigations.
Daba, Imiru T. and Duressa, Gemechis F.
Hybrid Algorithm for Singularly Perturbed Delay Parabolic Partial Differential Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
1, Article 21.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss1/21