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Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation 基于重心拉格朗日插值法求解非线性波方程
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s44198-024-00200-5
Hongwang Yuan, Xiyin Wang, Jin Li
{"title":"Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation","authors":"Hongwang Yuan, Xiyin Wang, Jin Li","doi":"10.1007/s44198-024-00200-5","DOIUrl":"https://doi.org/10.1007/s44198-024-00200-5","url":null,"abstract":"<p>In this paper, we deeply study the high-precision barycentric Lagrange interpolation collocation method to solve nonlinear wave equations. Firstly, we introduce the barycentric Lagrange interpolation and provide the differential matrix. Secondly, we construct a direct linearization iteration scheme to solve nonlinear wave equations. Once again, we use the barycentric Lagrange interpolation to approximate the (2+1) dimensional nonlinear wave equations and (3+1) dimensional nonlinear wave equations, and describe the matrix format for direct linearization iteration of the nonlinear wave equations. Finally, the comparative experiments show that the barycentric Lagrange interpolation collocation method for solving nonlinear wave equations have higher calculation accuracy and convergence rate.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options 为美式期权定价的分式布莱克-斯科尔斯方程的稳健数值模拟
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s44198-024-00207-y
S. M. Nuugulu, F. Gideon, K. C. Patidar
{"title":"A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options","authors":"S. M. Nuugulu, F. Gideon, K. C. Patidar","doi":"10.1007/s44198-024-00207-y","DOIUrl":"https://doi.org/10.1007/s44198-024-00207-y","url":null,"abstract":"<p>After the discovery of fractal structures of financial markets, fractional partial differential equations (fPDEs) became very popular in studying dynamics of financial markets. Available research results involves two key modelling aspects; firstly, derivation of tractable asset pricing models, those that closely reflects the actual dynamics of financial markets. Secondly, the development of robust numerical solution methods. Often times, most the effective models are of a nonlinear nature, and as such, reliable analytical solution methods are seldomly available. On the other hand, the accurate value of American options strongly lies on the unknown free boundaries associated with these types of derivative contracts. The free boundaries emanates from the flexibility of the early exercise features with American options. To the best of our knowledge, the approach of pricing American options under the fractional calculus framework has not been extensively explored in literature, and an obvious wider research gap still exist on the design of robust solution methods for pricing American option problems formulated under the fractional calculus framework. Therefore, this paper serve to propose a robust numerical scheme for solving time-fractional Black–Scholes PDEs for pricing American put option problems. The proposed scheme is based on the front-fixing algorithm, under which the early exercise boundaries are transformed into fixed boundaries, allowing for a simultaneous computation of optimal exercise boundaries and their corresponding fair premiums. Results herein indicate that, the proposed numerical scheme is consistent, stable, convergent with order <span>({mathcal {O}}(h^2,k))</span>, and also does guarantee positivity of solutions under all possible market conditions.\u0000</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Triple Mixed Integral Transformation and Applications for Initial-Boundary Value Problems 三重混合积分变换及其在初值-边界问题中的应用
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-13 DOI: 10.1007/s44198-024-00206-z
Chun Wang, Tian-Zhou Xu
{"title":"Triple Mixed Integral Transformation and Applications for Initial-Boundary Value Problems","authors":"Chun Wang, Tian-Zhou Xu","doi":"10.1007/s44198-024-00206-z","DOIUrl":"https://doi.org/10.1007/s44198-024-00206-z","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Design and Analysis of a Group of Correlative and Switchable Dual Memristor Hyperchaotic Systems 一组相关和可切换双膜片超混沌系统的设计与分析
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-12 DOI: 10.1007/s44198-024-00204-1
Jie Fang, Jiabin Wang, Na Fang, Yong Jiang
{"title":"Design and Analysis of a Group of Correlative and Switchable Dual Memristor Hyperchaotic Systems","authors":"Jie Fang, Jiabin Wang, Na Fang, Yong Jiang","doi":"10.1007/s44198-024-00204-1","DOIUrl":"https://doi.org/10.1007/s44198-024-00204-1","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141354704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
3-pre-Leibniz Algebras, Deformations and Cohomologies of Relative Rota-Baxter Operators on 3-Leibniz Algebras 3-前莱布尼兹代数、3-莱布尼兹代数上相对罗塔-巴克斯特算子的变形与同调
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-11 DOI: 10.1007/s44198-024-00198-w
Meiyan Hu, Shuai Hou, Lina Song, Yanqiu Zhou
{"title":"3-pre-Leibniz Algebras, Deformations and Cohomologies of Relative Rota-Baxter Operators on 3-Leibniz Algebras","authors":"Meiyan Hu, Shuai Hou, Lina Song, Yanqiu Zhou","doi":"10.1007/s44198-024-00198-w","DOIUrl":"https://doi.org/10.1007/s44198-024-00198-w","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141358048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dissipative Soliton Resonance: Adiabatic Theory and Thermodynamics 耗散孤子共振：绝热理论与热力学
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-10 DOI: 10.1007/s44198-024-00203-2
Vladimir L. Kalashnikov, Alexander Rudenkov, Evgeni Sorokin, Irina T. Sorokina
{"title":"Dissipative Soliton Resonance: Adiabatic Theory and Thermodynamics","authors":"Vladimir L. Kalashnikov, Alexander Rudenkov, Evgeni Sorokin, Irina T. Sorokina","doi":"10.1007/s44198-024-00203-2","DOIUrl":"https://doi.org/10.1007/s44198-024-00203-2","url":null,"abstract":"<p>We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg–Landau equation (CQGLE). Solutions in the closed analytical form in the spectral domain have the shape of Rayleigh–Jeans distribution for a positive (normal) dispersion. The DS parametric space forms a two-dimensional (or three-dimensional for the complex quintic nonlinearity) master diagram connecting the DS energy and a universal parameter formed by the ratio of four real and imaginary coefficients for dissipative and non-dissipative terms in CQGLE. The concept of dissipative soliton resonance (DSR) is formulated in terms of the master diagram, and the main signatures of transition to DSR are demonstrated and experimentally verified. We show a close analogy between DS and incoherent (semicoherent) solitons with an ensemble of quasi-particles confined by a collective potential. It allows applying the thermodynamical approach to DS and deriving the conditions for the DS energy scalability.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adaptive Fuzzy Control for Fractional-Order Networked Control Systems with Input Time Delay and Data Loss 有输入时间延迟和数据丢失的分数阶网络控制系统的自适应模糊控制
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-04 DOI: 10.1007/s44198-024-00201-4
Chunzhi Yang, Xiulan Zhang
{"title":"Adaptive Fuzzy Control for Fractional-Order Networked Control Systems with Input Time Delay and Data Loss","authors":"Chunzhi Yang, Xiulan Zhang","doi":"10.1007/s44198-024-00201-4","DOIUrl":"https://doi.org/10.1007/s44198-024-00201-4","url":null,"abstract":"<p>This paper considers the adaptive fuzzy control of fractional-order nonlinear networked control systems subjected to network-induced input delay and data loss. To approximate unknown functions, fuzzy logic systems are employed. Furthermore, the Pade approximation method and an intermediate variable are introduced to eliminate the impact of input delay, and an adaptive fuzzy controller is designed using backstepping technology. Based on fractional-order Lyapunov stability theory, the proposed method can ensure that all signals are uniformly ultimately bounded, and the tracking error can converge to a small region of the origin. Two simulation examples are provided to verify the viability of the control method.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bifurcation, Traveling Wave Solutions and Dynamical Analysis in the $$(2+1)$$ -Dimensional Extended Vakhnenko–Parkes Equation $$(2+1)$$维扩展瓦赫年科-帕克斯方程中的分岔、游波解和动力学分析
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-04 DOI: 10.1007/s44198-024-00202-3
Yan Sun, Juan-Juan Wu, Xiao-Yong Wen
{"title":"Bifurcation, Traveling Wave Solutions and Dynamical Analysis in the $$(2+1)$$ -Dimensional Extended Vakhnenko–Parkes Equation","authors":"Yan Sun, Juan-Juan Wu, Xiao-Yong Wen","doi":"10.1007/s44198-024-00202-3","DOIUrl":"https://doi.org/10.1007/s44198-024-00202-3","url":null,"abstract":"<p>This paper is concerned with the bifurcation of the traveling wave solutions, as well as the dynamical behaviors and physical property of the soliton solutions of the (2+1)-dimensional extended Vakhnenko–Parkes (eVP) equation. Firstly, based on the traveling wave transformation, the planar dynamical system corresponding to the (2+1)-dimensional eVP equation is derived, and then the singularity type and trajectory map of this system are obtained and analyzed. Based on the bifurcation of this system, the analytical expression for the periodic wave solution is given and shown graphically. Secondly, the <i>N</i>-soliton solutions are obtained via the bilinear method, and some important physical quantities and asymptotic analysis of one-soliton and two-soliton solutions are discussed. The results obtained in this paper might be useful for understanding the propagation of high-frequency waves.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weak Signal Detection Application Based on Incommensurate Fractional-Order Duffing System 基于不相称分序达芬系统的弱信号检测应用
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-05-27 DOI: 10.1007/s44198-024-00197-x
Hong-Cun Mao, Yu-Ling Feng, Xiao-Qian Wang, Zhi-Hai Yao
{"title":"Weak Signal Detection Application Based on Incommensurate Fractional-Order Duffing System","authors":"Hong-Cun Mao, Yu-Ling Feng, Xiao-Qian Wang, Zhi-Hai Yao","doi":"10.1007/s44198-024-00197-x","DOIUrl":"https://doi.org/10.1007/s44198-024-00197-x","url":null,"abstract":"<p>The Duffing Chaos System can detect weak signals that are obscured by Gaussian noise because it is sensitive to specific signal functions and can withstand noise. In this paper, we investigate the use of intermittent chaotic phenomena in fractional-order incommensurate Duffing chaotic systems for weak signal detection. This new intermittent chaotic state has not appeared in integer-order Duffing systems before, so this phenomenon reflects the superiority of fractional-order Duffing systems. We start by giving the incommensurate fractional-order Duffing system’s weak signal detection model. Then design a time series-based judgment method that successfully separates chaotic, intermittent chaotic, and limit cycle states. Finally, the intermittent chaotic of fractional-order detection system is used to determine the amplitude and frequency of the weak signals to calculate the detection performance. The results show that the weak signal can be detected at a maximum signal-to-noise ratio of <span>(-)</span>13.26 dB for single-detection oscillator amplitude detection. When detecting the frequency, a single-detection oscillator can detect the frequency range of 1050 rad/s, proving that the fractional-order chaos detection system is better than the integer-order chaos detection system.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Dynamic Bifurcation for the Granulation Convection in Cylindrical Coordinates 圆柱坐标下粒状对流的动态分岔
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2024-05-22 DOI: 10.1007/s44198-024-00191-3
Junyan Li, Limei Li, Rui-xin Wu
{"title":"The Dynamic Bifurcation for the Granulation Convection in Cylindrical Coordinates","authors":"Junyan Li, Limei Li, Rui-xin Wu","doi":"10.1007/s44198-024-00191-3","DOIUrl":"https://doi.org/10.1007/s44198-024-00191-3","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141110960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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