随机扰动下三阶MQ拟插值在导数逼近中的应用研究

随机扰动下三阶MQ拟插值在导数逼近中的应用研究

Application of Cubic MQ Quasi-Interpolation in Derivative Approximations Under Random Perturbation

摘要/Abstract

图/表 9

参考文献 18

Metrics

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 180-188.

张胜良^1,^*(),钱艳艳²()

¹南京林业大学经济管理学院南京 210037
²南京林业大学理学院南京 210037

收稿日期:2024-03-22 修回日期:2024-07-09 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 张胜良,E-mail:10110180035@fudan.edu.cn
作者简介:钱艳艳,E-mail:qianyanyan@njfu.edu.cn
基金资助:
教育部人文社会科学研究 `基于两种市场决策机制的林业碳汇价值评估研究-实物期权模型的改进与应用'项目(21YJC790162);江苏省社科基金 "双碳" 目标下苏北杨树产业碳汇价值实现机制及支持政策研究(22EYB010)

Shengliang Zhang^1,^*(),Yanyan Qian²()

¹College of Economics and Management, Nanjing Forestry University, Nanjing 210037
²College of Science, Nanjing Forestry University, Nanjing 210037

Received:2024-03-22 Revised:2024-07-09 Online:2025-02-26 Published:2025-01-08
Supported by:
Improvement and application of real option model'(21YJC790162);Jiangsu Provincial Social Science Foundation(22EYB010)

摘要：

该文基于三阶 MQ (multiquadric) 拟插值算子, 提出了在随机扰动背景下有效逼近高阶导数的数值方法, 并给出了相应的数值算例和误差估计. 试验表明, 该方法相比已有方法精度更高、更稳定、更有效.

关键词: 导数逼近, 随机扰动, MQ 拟插值, 误差估计.

Abstract:

This paper proposes a numerical method that can effectively approximate high-order derivatives under random perturbation based on the cubic MQ (multiquadric) quasi-interpolation operator. Corresponding numerical examples and error estimates are given. Numerical experimental results show that the proposed method is more accurate, more stable and more effective than the existing methods.

Key words: derivative approximation, random perturbation, multi-quadric quasi-interpolation, error estimations.

中图分类号:

O241.5

张胜良, 钱艳艳. 随机扰动下三阶MQ拟插值在导数逼近中的应用研究[J]. 数学物理学报, 2025, 45(1): 180-188.

Shengliang Zhang, Yanyan Qian. Application of Cubic MQ Quasi-Interpolation in Derivative Approximations Under Random Perturbation[J]. Acta mathematica scientia,Series A, 2025, 45(1): 180-188.

表 1

三阶 MQ 形状参数 $c$ 的敏感性分析"

表 1

图1

图2

表 2

图3

图4

图5

表 3

形状参数 $c$ 的敏感性分析"

表 3

表 4

三阶 MQ 和 FDM 方法在 $t=1$ 时的数值结果对比"

表 4

[1]	Beatson R K, Powell M J D. Univariate multiquadric approximation: Quasi-interpolation to scattered data. Constructive Approximation, 1992, 8(3): 275-288
[2]	Buhmann M D. Multivariate interpolation in odd-dimensional Euclidean spaces using multiquadrics. Constructive Approximation, 1990, 6(1): 21-34
[3]	Chen R H, Wu Z M. Applying multiquadric quasi-interpolation to solve Burgers' equation. Applied Mathematics and Computation, 2006, 172(1): 472-484
[4]	Chen W, Fu Z J, Chen C S. Recent Advances in Radial Basis Function Collocation Methods. Berlin: Springer, 2014
[5]	Fasshauer G E. Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers & Mathematics with Applications, 2002, 43(3-5): 423-438
[6]	Fasshauer G E, Zhang J G. On choosing "optimal" shape parameters for RBF approximation. Numerical Algorithms, 2007, 45(1-4): 345-368
[7]	Franke R. Scattered data interpolation: tests of some methods. Mathematics of Computation, 1982, 38(357): 181-200
[8]	Gao Q J, Wu Z M, Zhang S G. Applying multiquadric quasi-interpolation for boundary detection. Computers & Mathematics with Applications, 2011, 62(12): 4356-4361
[9]	Godunov S K, Bohachevsky I. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics. Matematičeskij Sbornik, 1959, 47(3): 271-306
[10]	Hardy R L. Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research, 1971, 76(8): 1905-1915
[11]	Hon Y C, Mao X Z. An efficient numerical scheme for Burgers' equation. Applied Mathematics and Computation, 1998, 95(1): 37-50
[12]	Ma L M, Wu Z M. Approximation to the k-th derivatives by multiquadric quasi-interpolation method. Journal of Computational and Applied Mathematics, 2009, 231(2): 925-932
[13]	Ma L M, Wu Z M. Stability of multiquadric quasi-interpolation to approximate high order derivatives. Science China Mathematics, 2010, 53(4): 985-992
[14]	Mittal R C, Tripathi A. Numerical solutions of generalized Burgers-Fisher and generalized Burgers-Huxley equations using collocation of cubic B-splines. Int J Comput Math, 2015, 92(5): 1053-1077
[15]	Wu Z M, Schaback R. Shape preserving properties and convergence of univariate multiquadric quasi-interpolation. Acta Mathematicae Applicatae Sinica, 1994, 10(4): 441-446
[16]	Wu Z M, Zhang S L. Conservative multiquadric quasi-interpolation method for Hamiltonian wave equations. Engineering Analysis with Boundary Elements, 2013, 37(7/8): 1052-1058
[17]	Zhang S L, Yang H Q, Yang Y. A multiquadric quasi-interpolations method for CEV option pricing model. Journal of Computational and Applied Mathematics, 2019, 347: 1-11 doi: 10.1016/j.cam.2018.03.046
[18]	Zhu C G, Kang W S. Numerical solution of Burgers-Fisher equation by cubic B-spline quasi-interpolation. Applied Mathematics and Computation, 2010, 216(9): 2679-2686

Just accepted

Online first

Just accepted

Online first

Viewed

Full text

	From	local

	Times	85
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	37

From	Others	local

Times	34	3
Rate	92%	8%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed