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New optimal adaptive stepsize algorithm for solving black-scholes equation | ||
| Computational Methods for Differential Equations | ||
| مقاله 9، دوره 14، شماره 2، تیر 2026، صفحه 633-651 اصل مقاله (12.92 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65090.2974 | ||
| نویسندگان | ||
| Marziyeh Alishahi؛ Majid Yarahmadi* | ||
| Department of Mathematics and Computer Science, Lorestan University, Khorramabad, Lorestan 44316-68151, Iran. | ||
| چکیده | ||
| In this paper, a new algorithm is designed based on a state feedback global error control system, Laplace trans form, order reduction method, and k-step numerical integration methods to numerically solve the Black-Scholes equation. For this purpose, the Black-Scholes equation is converted into a first-order system of ordinary differ ential equations by using the Laplace transform and order reduction method. Also, a new robust linear optimal adaptive global error control dynamic for designing an adaptive time variant step size sequence is modeled and a corresponding optimal control law based on robust and optimal eigenvalue assignment is designed. The proposed optimal control law guarantees the absolute stability of the implemented k-step numerical integrator methods. Finally, the transformed approximate solution of the Black-Scholes equation has been obtained using the Stefhest inverse Laplace transformation algorithm. The simulation examples show that the optimal control of global error under a given tolerance level, the guarantee of absolute stability, and the best approximation of sensitivity analysis indexes for the proposed approximate solution of the Black-Scholes equation is among the important advantages of the proposed method. | ||
| کلیدواژهها | ||
| Black-Scholes equation؛ Laplace transform؛ Global error؛ Numerical integration؛ State feedback؛ Adaptive step size؛ Eigenvalues as signment؛ Certainty matrix | ||
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آمار تعداد مشاهده مقاله: 395 تعداد دریافت فایل اصل مقاله: 206 |
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