Stability and Benchmark-Based Convergence Assessment of Extended Cubic B-Spline Collocation for Time-Fractional Advection-Diffusion Equations
DOI:
https://doi.org/10.33003/fjs-2026-1019-6252Keywords:
Caputo Derivative, Time Fractional Advection - Difussion, Extended Cubic B-Splines, Implicit Collocation, Fourier Stability, Benchmark VerificationAbstract
This study examines a fully implicit finite difference scheme based on extended cubic B-spline collocation for solving one-dimensional tim236e-fractional advection–diffusion equations. The time-fractional derivative is approximated using the Caputo formulation with the L1 discretization scheme, while the spatial derivatives are approximated using extended cubic B-spline basis functions. The resulting fully discrete system incorporates the memory effects of the fractional derivative together with the prescribed initial and boundary conditions. The stability and convergence properties of the scheme are examined through Fourier analysis and mathematical approximation estimates under appropriate assumptions. The numerical performance is assessed using two benchmark problems with known analytical solutions. Comparisons of the published numerical and exact solutions demonstrate good agreement, while the reported error norms and spatial refinement results indicate decreasing numerical errors as the spatial grid is refined. The findings support the accuracy and applicability of the fully implicit extended cubic B-spline collocation scheme for the considered benchmark problems
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Copyright (c) 2026 Audu Abdulmalik Onubedo, Nasiru Mohammed, Idris Babaji Muhammad
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