A Novel Numerical Algorithm for Singularly Perturbed Parabolic Problems With Discontinuous Convection Coefficient and Source Terms

Mousa J. Huntul and Imiru Takele Daba

Advances in Mathematical Physics, 2026, vol. 2026, 1-15

Abstract: In this work, a novel numerical algorithm is presented to solve singularly perturbed parabolic problems with discontinuous convection coefficients and source terms. The problem is approximated using the Crank–Nicolson method in the temporal direction on a uniform mesh and the novel finite difference method in spatial direction. The parameter uniform convergence of the proposed scheme is investigated. The method is shown to be second-order accurate in both the temporal and spatial directions. It is also shown that the proposed method is better than some existing methods in the literature. The numerical experiments confirm the theoretical findings.MSC2020 Classification: 35B25, 65M06, 65N12

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:4417340

DOI: 10.1155/admp/4417340

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