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New Optimal Adaptive Step size Algorithm for Solving Black-Scholes Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 اردیبهشت 1404 اصل مقاله (13.67 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 state feedback global error control system, Laplace transform, 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 differential 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 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 approximating 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 are among the important advantages of the proposed method. | ||
| کلیدواژه‌ها | ||
| Global error؛ State feedback؛ Adaptive step size؛ Eigenvalues assignment؛ Certainty matrix | ||
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آمار تعداد مشاهده مقاله: 22 تعداد دریافت فایل اصل مقاله: 35 |
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