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Quartic spline technique for time-dependent convection-diffusion of singularly perturbed problems
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DOI：10.1016/j.rineng.2026.112303.png)
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Abstract
En 中文
• A fourth-order accurate finite difference scheme is developed for time-fractional singularly perturbed convection–diffusion problems. • The Caputo fractional derivative is discretized using an implicit Euler approach, ensuring stability in time. • A quartic non-polynomial spline with fitted parameters is employed for spatial discretization on a uniform mesh. • Parameter-uniform convergence is rigorously established through truncation error and stability analysis. • Numerical experiments confirm the superior accuracy of the proposed method compared with existing schemes.
Keywords:
Two-parameter fitting
Quartic spline
Parabolic equation
Double mesh principle
Parameter-uniform convergence
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