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Volume 14
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10.3390/math14010017
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Article

Exponentially Fitted Midpoint Scheme for a Stochastic Oscillator

by
Yaru Wang
1,2,
Zhenyu Lang
1,2,
XiuLing Yin
2,* and
Zihan Zhao
1,2
1
School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
2
School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(1), 17; https://doi.org/10.3390/math14010017 (registering DOI)
Submission received: 6 November 2025 / Revised: 7 December 2025 / Accepted: 18 December 2025 / Published: 21 December 2025
(This article belongs to the Special Issue Advances in Stochastic Differential Equations and Applications)
Versions Notes

Abstract

In this paper, we propose the exponentially fitted midpoint scheme for the stochastic oscillator. This scheme is first-order strongly convergent and it preserves symplectic. It can effectively simulate the oscillatory behavior of stochastic oscillators, and its second moment grows linearly with time. In addition, we also propose a two-parameter estimation method by analyzing the expectation and variance in the discrete scheme. Numerical experiments are given to verify effectiveness of the exponential fitting method and parameter estimation methods based on this scheme.
Keywords: exponentially fitted midpoint scheme; symplectic scheme; convergence; Euler-Maruyama scheme; parameter estimation exponentially fitted midpoint scheme; symplectic scheme; convergence; Euler-Maruyama scheme; parameter estimation

Share and Cite

MDPI and ACS Style

Wang, Y.; Lang, Z.; Yin, X.; Zhao, Z. Exponentially Fitted Midpoint Scheme for a Stochastic Oscillator. Mathematics 2026, 14, 17. https://doi.org/10.3390/math14010017

AMA Style

Wang Y, Lang Z, Yin X, Zhao Z. Exponentially Fitted Midpoint Scheme for a Stochastic Oscillator. Mathematics. 2026; 14(1):17. https://doi.org/10.3390/math14010017

Chicago/Turabian Style

Wang, Yaru, Zhenyu Lang, XiuLing Yin, and Zihan Zhao. 2026. "Exponentially Fitted Midpoint Scheme for a Stochastic Oscillator" Mathematics 14, no. 1: 17. https://doi.org/10.3390/math14010017

APA Style

Wang, Y., Lang, Z., Yin, X., & Zhao, Z. (2026). Exponentially Fitted Midpoint Scheme for a Stochastic Oscillator. Mathematics, 14(1), 17. https://doi.org/10.3390/math14010017

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