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Efficient hybridized numerical scheme for singularly perturbed parabolic reaction–diffusion equations with Robin boundary conditions
- Source :
- Partial Differential Equations in Applied Mathematics, Vol 10, Iss , Pp 100662- (2024)
- Publication Year :
- 2024
- Publisher :
- Elsevier, 2024.
-
Abstract
- An efficient numerical technique for a singularly perturbed parabolic reaction–diffusion problem with Robin type boundary conditions is presented in this work. The governing problem is discretized using the implicit Euler technique in time direction and a hybrid numerical technique that comprises a central finite difference method in the outer region and a cubic spline in compression method in the boundary layer regions in space direction. We use Shishkin-type meshes in the space domain to resolve the layers. The Robin type boundary conditions are handled using the second-order method. The totally discretized problem is well examined for stability and convergence. The use Bakhvalov–Shishkin and Vulanović–Shishkin meshes yields a more efficient and second-order convergence whereas Shishkin mesh produces almost second-order convergent solutions. Two test examples are computed. The current method has been compared to other methods in the scientific community.
Details
- Language :
- English
- ISSN :
- 26668181
- Volume :
- 10
- Issue :
- 100662-
- Database :
- Directory of Open Access Journals
- Journal :
- Partial Differential Equations in Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.3ba66c8edd9e456ea9894a817f82e959
- Document Type :
- article
- Full Text :
- https://doi.org/10.1016/j.padiff.2024.100662