A Fast Computational Scheme for Solving the Temporal-Fractional Black–Scholes Partial Differential Equation
In this work, we propose a fast scheme based on higher order discretizations on graded meshes for resolving the temporal-fractional partial differential equation (PDE), which benefits the memory feature of fractional calculus. To avoid excessively increasing the number of discretization points, such...
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Published in | Fractal and fractional Vol. 7; no. 4; p. 323 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Basel
MDPI AG
01.04.2023
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Subjects | |
Online Access | Get full text |
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Summary: | In this work, we propose a fast scheme based on higher order discretizations on graded meshes for resolving the temporal-fractional partial differential equation (PDE), which benefits the memory feature of fractional calculus. To avoid excessively increasing the number of discretization points, such as the standard finite difference or meshfree methods, and, at the same time, to increase the efficiency of the solver, we employ discretizations on spatially non-uniform meshes with an attention on the non-smoothness area of the underlying asset. Therefore, the PDE problem is transformed to a linear system of algebraic equations. We perform numerical simulations to observe and check the behavior of the presented scheme in contrast to the existing methods. |
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ISSN: | 2504-3110 2504-3110 |
DOI: | 10.3390/fractalfract7040323 |