HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL

Muhammed Fayis P.; Fathima Hida M. P. Meethal; Suresh Kumar Nadupuri

HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL

Abstract

This work is focused on the construction of {numerical schemes with higher-order accuracy in space and time to solve} the time-fractional Black-Scholes model that governs the price of European options. We develop three numerical schemes utilizing the fourth-order {Pad\'e} approximation, a fourth-order Taylor's compact difference scheme and a fourth-order compact exponential scheme for spatial discretization. We employ $L1\text{-}2\text{-}3$ approximation of order $4-\alpha,~0<\alpha<1$, to discretize the time-fractional derivative. In addition, the solvability, convergence, and stability of these numerical schemes are established. Numerical experiments are conducted to demonstrate the accuracy of the proposed schemes and validate the theoretical findings. The new proposed schemes offer higher and better accuracy.

Keywords

Thanks

The authors express sincere gratitude to anonymous referees for their valuable suggestions, which greatly helped to improve the quality of the manuscript.

References

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Partial Differential Equations

Journal Section

Research Article

Authors

Muhammed Fayis P. This is me
0009-0004-3485-911X
India

Fathima Hida M. P. Meethal This is me
0009-0003-9878-157X
India

Suresh Kumar Nadupuri ^* This is me
0000-0001-7020-2749
India

Publication Date

May 4, 2026

Submission Date

March 28, 2025

Acceptance Date

July 21, 2025

Published in Issue

Year 2026 Volume: 16 Number: 5

IZ

https://izlik.org/JA77ND49FN

Cite

RIS / Bibtex

APA

P., M. F., Meethal, F. H. M. P., & Nadupuri, S. K. (2026). HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL. TWMS Journal of Applied and Engineering Mathematics, 16(5), 640-669. https://izlik.org/JA77ND49FN

AMA

1.P. MF, Meethal FHMP, Nadupuri SK. HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL. JAEM. 2026;16(5):640-669. https://izlik.org/JA77ND49FN

Chicago

P., Muhammed Fayis, Fathima Hida M. P. Meethal, and Suresh Kumar Nadupuri. 2026. “HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL”. TWMS Journal of Applied and Engineering Mathematics 16 (5): 640-69. https://izlik.org/JA77ND49FN.

EndNote

P. MF, Meethal FHMP, Nadupuri SK (May 1, 2026) HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL. TWMS Journal of Applied and Engineering Mathematics 16 5 640–669.

IEEE

[1]M. F. P., F. H. M. P. Meethal, and S. K. Nadupuri, “HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL”, JAEM, vol. 16, no. 5, pp. 640–669, May 2026, [Online]. Available: https://izlik.org/JA77ND49FN

ISNAD

P., Muhammed Fayis - Meethal, Fathima Hida M. P. - Nadupuri, Suresh Kumar. “HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL”. TWMS Journal of Applied and Engineering Mathematics 16/5 (May 1, 2026): 640-669. https://izlik.org/JA77ND49FN.

JAMA

1.P. MF, Meethal FHMP, Nadupuri SK. HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL. JAEM. 2026;16:640–669.

MLA

P., Muhammed Fayis, et al. “HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 5, May 2026, pp. 640-69, https://izlik.org/JA77ND49FN.

Vancouver

1.Muhammed Fayis P., Fathima Hida M. P. Meethal, Suresh Kumar Nadupuri. HIGHER-ORDER ACCURATE COMPACT SCHEMES AND ANALYSIS FOR THE TIME-FRACTIONAL BLACK-SCHOLES MODEL. JAEM [Internet]. 2026 May 1;16(5):640-69. Available from: https://izlik.org/JA77ND49FN