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Modified Cubic B-spline Based Differential Quadrature Methods for Time-fractional Black-Scholes Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 خرداد 1405 اصل مقاله (2.06 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.71605.3598 | ||
| نویسندگان | ||
| Nizamudheen V1؛ Riyasudheen TK* 2؛ Noufal Asharaf3؛ Shefeeq T4 | ||
| 1Department of Mathematics, Farook College (Autonomous) affiliated to University of Calicut, Kozhikode, 673632, India. | ||
| 2Department of Computational Science and Humanities, Indian Institute of Information Technology Kottayam, Valavoor, Kottayam 686635, Kerala, India. | ||
| 3Department of Mathematics, CUSAT (Cochin University of Science and Technology), Cochin, 682022, India. | ||
| 4Department of Mathematics, Farook College (Autonomous) affiliated to University of Calicut, Kozhikode, 673632, India | ||
| چکیده | ||
| The time-fractional Black–Scholes equation (TFBSE) is indented to price the options for which the underlying price fluctuates within a correlated fractal transmission system. Although the TFBSE is an influential approach for grasping the long-term memory traits of financial markets, the non-local nature of fractional derivatives makes significant challenges in finding an accurate solution. We perform an efficient use of the differential quadrature method (DQM) based on modified cubic B-splines to solve the TFBSE governing European options. This paper constructs an algorithm by the combination of time fractional discretization using the finite difference method L1 and space discretization using the modified cubic B-spline-based differential quadrature method. Uniform meshes are considered for the discretization of both temporal and spatial domains. Theoretical stability has been established by finding an estimate for the maximum norm of the inverse operator regardless of the involvement of the mesh parameters. We trigger the Nuemann series theorem to obtain a uniform bound for the inverse operator under reasonable conditions on the mesh parameters. The numerical illustrations show that this implicit numerical method exhibits a fourth-order convergence in the space direction and the order 2 − α in time. Moreover, we observe an enhancement in order of spatial convergence whenever α tends to 0. The results obtained are then compared with existing popular techniques to demonstrate the accuracy of modified cubic B-spline-based DQM. | ||
| کلیدواژهها | ||
| Black-Scholes equation؛ time-fractional Black-Scholes equation؛ differential quadrature method؛ modified cubic B-splines | ||
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آمار تعداد مشاهده مقاله: 107 تعداد دریافت فایل اصل مقاله: 93 |
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