In this article, a steady-state fractional-order boundary-value problem is considered with a fractional convection term. The highest-order derivative term involves a mixed-fractional derivative, which appears as a combination of a first-order classical derivative and a Caputo fractional derivative. We propose an L1 scheme over a uniform mesh for the numerical solution of the fractional differential equation. With the help of a properly chosen barrier function, we discuss error analysis and prove that the proposed method converges with almost first-order. The proposed scheme is also applied to a semilinear fractional differential equation. Numerical experiments are presented to validate the proposed method.
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Seal, A. and Natesan, S. (2026). An accurate finite-difference scheme for the numerical solution of a fractional differential equation. Computational Methods for Differential Equations, 14(1), 165-187. doi: 10.22034/cmde.2024.61919.2699
MLA
Seal, A. , and Natesan, S. . "An accurate finite-difference scheme for the numerical solution of a fractional differential equation", Computational Methods for Differential Equations, 14, 1, 2026, 165-187. doi: 10.22034/cmde.2024.61919.2699
HARVARD
Seal, A., Natesan, S. (2026). 'An accurate finite-difference scheme for the numerical solution of a fractional differential equation', Computational Methods for Differential Equations, 14(1), pp. 165-187. doi: 10.22034/cmde.2024.61919.2699
CHICAGO
A. Seal and S. Natesan, "An accurate finite-difference scheme for the numerical solution of a fractional differential equation," Computational Methods for Differential Equations, 14 1 (2026): 165-187, doi: 10.22034/cmde.2024.61919.2699
VANCOUVER
Seal, A., Natesan, S. An accurate finite-difference scheme for the numerical solution of a fractional differential equation. Computational Methods for Differential Equations, 2026; 14(1): 165-187. doi: 10.22034/cmde.2024.61919.2699
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