Numerical Schemes Based on Splines for Two-Dimensional Singularly Perturbed Elliptic Partial Differential Equations With Mixed Shifts

Vivek K. and R. Nageshwar Rao

International Journal of Differential Equations, 2026, vol. 2026, 1-16

Abstract: In this study, we considered a singular perturbation problem of two-dimensional, linear elliptic partial differential equations having both positive and negative shifts in both directions of the reaction terms, whose solution exhibits characteristic boundary layers. The shift terms are approximated using a Taylor series, and the resultant elliptic equation is treated with a fitted operator spline in tension and a fitted operator spline in compression on a uniform mesh to establish uniform estimates. The effect of the positive and negative shift on the behavior of the solution is explained by executing numerical experiments on three test problems.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:6439876

DOI: 10.1155/ijde/6439876

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