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 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 on a semilinear fractional differential equation. Numerical experiments are presented to validate the proposed method.
Seal, A., & Natesan, S. (2024). An accurate finite-difference scheme for the numerical solution of a fractional differential equation. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2024.61919.2699
MLA
Aniruddha Seal; Srinivasan Natesan. "An accurate finite-difference scheme for the numerical solution of a fractional differential equation". Computational Methods for Differential Equations, , , 2024, -. doi: 10.22034/cmde.2024.61919.2699
HARVARD
Seal, A., Natesan, S. (2024). 'An accurate finite-difference scheme for the numerical solution of a fractional differential equation', Computational Methods for Differential Equations, (), pp. -. 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, 2024; (): -. doi: 10.22034/cmde.2024.61919.2699
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