Pub Date : 2024-11-23DOI: 10.1016/j.aml.2024.109393
Chunchi Liu , Yizhong Sun , Jiaping Yu
This paper investigates a fully parallel decoupled approach of the discrete stabilized finite element method for the time-dependent Stokes–Darcy problem. By introducing an auxiliary function, we rigorously demonstrate that the parallel algorithm is unconditionally stable.
{"title":"SAV unconditional stable estimate of parallel decoupled stabilized finite element algorithm for the fully mixed Stokes–Darcy problems","authors":"Chunchi Liu , Yizhong Sun , Jiaping Yu","doi":"10.1016/j.aml.2024.109393","DOIUrl":"10.1016/j.aml.2024.109393","url":null,"abstract":"<div><div>This paper investigates a fully parallel decoupled approach of the discrete stabilized finite element method for the time-dependent Stokes–Darcy problem. By introducing an auxiliary function, we rigorously demonstrate that the parallel algorithm is unconditionally stable.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109393"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.aml.2024.109390
Ziliang Yang , Jiabao Su , Mingzheng Sun
In this paper, we consider the following elliptic problem where the nonlinearity satisfies the Ambrosetti–Rabinowitz condition. Using an additional growth condition of at a bounded region, we can obtain five nontrivial solutions of by applying homological linking arguments and Morse theory.
本文考虑以下椭圆问题 -Δu=f(x,u),inΩ,u=0,on∂Ω,(P) 其中非线性 f 满足 Ambrosetti-Rabinowitz 条件。利用 f 在有界区域的附加增长条件，我们可以通过应用同调联系论证和莫尔斯理论得到 (P) 的五个非微观解。
{"title":"Multiple solutions of the Ambrosetti–Rabinowitz problem","authors":"Ziliang Yang , Jiabao Su , Mingzheng Sun","doi":"10.1016/j.aml.2024.109390","DOIUrl":"10.1016/j.aml.2024.109390","url":null,"abstract":"<div><div>In this paper, we consider the following elliptic problem <span><math><mrow><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mtext>on</mtext><mspace></mspace><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></mrow></math></span> where the nonlinearity <span><math><mi>f</mi></math></span> satisfies the Ambrosetti–Rabinowitz condition. Using an additional growth condition of <span><math><mi>f</mi></math></span> at a bounded region, we can obtain five nontrivial solutions of <span><math><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></math></span> by applying homological linking arguments and Morse theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109390"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.aml.2024.109392
Yupeng Qin , Zhen Wang , Li Zou
The present work concerns with the higher dimensional Rayleigh–Plesset equation for describing the nonlinear dynamics of gas-filled hyper-spherical bubbles in an ideal fluid. A strict qualitative analysis is made by means of the bifurcation theory of dynamic system, indicating that the bubble oscillation type is periodic. An analytical approach based on elliptic function is suggested to construct parametric analytical solution with arbitrary space dimension , polytropic exponent and surface tension to the normalized higher dimensional Rayleigh–Plesset equation. The new obtained analytical solution extends the known ones for arbitrary (or some special cases of) and without considering the effect of surface tension. In addition, we also discuss the dynamic characteristics for the oscillating hyper-spherical bubbles.
{"title":"Qualitative analysis and analytical solution for higher dimensional gas-filled hyper-spherical bubbles in an ideal fluid","authors":"Yupeng Qin , Zhen Wang , Li Zou","doi":"10.1016/j.aml.2024.109392","DOIUrl":"10.1016/j.aml.2024.109392","url":null,"abstract":"<div><div>The present work concerns with the higher dimensional Rayleigh–Plesset equation for describing the nonlinear dynamics of gas-filled hyper-spherical bubbles in an ideal fluid. A strict qualitative analysis is made by means of the bifurcation theory of dynamic system, indicating that the bubble oscillation type is periodic. An analytical approach based on elliptic function is suggested to construct parametric analytical solution with arbitrary space dimension <span><math><mi>N</mi></math></span>, polytropic exponent <span><math><mi>κ</mi></math></span> and surface tension <span><math><mi>σ</mi></math></span> to the normalized higher dimensional Rayleigh–Plesset equation. The new obtained analytical solution extends the known ones for arbitrary (or some special cases of) <span><math><mi>N</mi></math></span> and <span><math><mi>κ</mi></math></span> without considering the effect of surface tension. In addition, we also discuss the dynamic characteristics for the oscillating hyper-spherical bubbles.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109392"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.aml.2024.109389
Anbiao Zeng, Guangze Gu
We consider the following fractional Schrödinger–Poisson system where is a fixed constant, is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.
{"title":"Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems","authors":"Anbiao Zeng, Guangze Gu","doi":"10.1016/j.aml.2024.109389","DOIUrl":"10.1016/j.aml.2024.109389","url":null,"abstract":"<div><div>We consider the following fractional Schrödinger–Poisson system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mi>ϕ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>ϕ</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is a fixed constant, <span><math><mi>f</mi></math></span> is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109389"},"PeriodicalIF":2.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-21DOI: 10.1016/j.aml.2024.109388
Zhihao Sheng , Yang Liu , Yonghai Li
In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter and a new variable parameter . We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.
{"title":"A double-parameter shifted convolution quadrature formula and its application to fractional mobile/immobile transport equations","authors":"Zhihao Sheng , Yang Liu , Yonghai Li","doi":"10.1016/j.aml.2024.109388","DOIUrl":"10.1016/j.aml.2024.109388","url":null,"abstract":"<div><div>In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter <span><math><mi>θ</mi></math></span> and a new variable parameter <span><math><mi>δ</mi></math></span>. We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109388"},"PeriodicalIF":2.9,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109380
Shubin Yu
We consider the existence of positive solutions for following Kirchhoff equation where , is the exterior of the unit ball in and . It is well-known that if , by standard minimization method on the Nehari manifold, one can obtain a positive radial solution. In present paper, we prove the existence of positive radial solutions for . This is the first contribution to the Kirchhoff equation in exterior domains provided that
{"title":"A new observation on the positive solutions for Kirchhoff equations in the exterior of a ball","authors":"Shubin Yu","doi":"10.1016/j.aml.2024.109380","DOIUrl":"10.1016/j.aml.2024.109380","url":null,"abstract":"<div><div>We consider the existence of positive solutions for following Kirchhoff equation <span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mtext>on</mtext><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span> where <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>Ω</mi><mo>=</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>:</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>></mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span> is the exterior of the unit ball in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> and <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. It is well-known that if <span><math><mrow><mn>4</mn><mo><</mo><mi>p</mi><mo><</mo><mi>∞</mi></mrow></math></span>, by standard minimization method on the Nehari manifold, one can obtain a positive radial solution. In present paper, we prove the existence of positive radial solutions for <span><math><mrow><mn>2</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>4</mn></mrow></math></span>. This is the first contribution to the Kirchhoff equation in exterior domains provided that <span><math><mrow><mn>2</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>4</mn><mo>.</mo></mrow></math></span></div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109380"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109383
Xin Zhang , Xiaofeng Li , Guoli Ma
The building of the national communication infrastructure and growing demand for data traffic both depend heavily on the advancement of optical soliton communication technology. In particular, by studying the interaction of optical solitons, some methods of controlling optical solitons can be explored to design more stable and efficient optical communication systems. In this paper, the interactions between optical solitons are studied based on the theory of generalized Schrödinger–Hirota equation. By studying the amplitude ratio, spacing and phase difference of the optical solitons, the interactions between the optical solitons occurring in the optical fiber transmission process are attenuated. The noninteraction transmission of optical solitons are realized with small spacing between them. The conclusions of this paper are not only of great significance for the in-depth understanding of the nature of optical soliton interactions, but also of great practical value for promoting the application of optical solitons in optical communications and other fields.
{"title":"Optical soliton noninteraction transmission in optical communication systems","authors":"Xin Zhang , Xiaofeng Li , Guoli Ma","doi":"10.1016/j.aml.2024.109383","DOIUrl":"10.1016/j.aml.2024.109383","url":null,"abstract":"<div><div>The building of the national communication infrastructure and growing demand for data traffic both depend heavily on the advancement of optical soliton communication technology. In particular, by studying the interaction of optical solitons, some methods of controlling optical solitons can be explored to design more stable and efficient optical communication systems. In this paper, the interactions between optical solitons are studied based on the theory of generalized Schrödinger–Hirota equation. By studying the amplitude ratio, spacing and phase difference of the optical solitons, the interactions between the optical solitons occurring in the optical fiber transmission process are attenuated. The noninteraction transmission of optical solitons are realized with small spacing between them. The conclusions of this paper are not only of great significance for the in-depth understanding of the nature of optical soliton interactions, but also of great practical value for promoting the application of optical solitons in optical communications and other fields.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109383"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109386
Xiaohua Jing , Junxiong Jia , Xueli Song
This article is concerned with the uniqueness of simultaneously determining the fractional order of the derivative in time, diffusion coefficient, and Robin coefficient, in one-dimensional time-fractional diffusion equations with derivative order and non-zero boundary conditions. The measurement data, which is the solution to the initial–boundary value problem, is observed at a single boundary point over a finite time interval. Based on the expansion of eigenfunctions for the solution to the forward problem and the asymptotic properties of the Mittag-Leffler function, the uniqueness of the fractional order is established. Subsequently, the uniqueness of the eigenvalues and the absolute value of the eigenfunction evaluated at for the associated operator are demonstrated. Then, the uniqueness of identifying the diffusion coefficient and the Robin coefficient is proven via an inverse boundary spectral analysis for the eigenvalue problem of the spatial differential operator. The results show that the uniqueness of three parameters can be simultaneously determined using limited boundary observations at a single spatial endpoint over a finite time interval, without imposing any constraints on the eigenfunctions of the spatial differential operator.
{"title":"Simultaneous uniqueness identification of the fractional order and diffusion coefficient in a time-fractional diffusion equation","authors":"Xiaohua Jing , Junxiong Jia , Xueli Song","doi":"10.1016/j.aml.2024.109386","DOIUrl":"10.1016/j.aml.2024.109386","url":null,"abstract":"<div><div>This article is concerned with the uniqueness of simultaneously determining the fractional order of the derivative in time, diffusion coefficient, and Robin coefficient, in one-dimensional time-fractional diffusion equations with derivative order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and non-zero boundary conditions. The measurement data, which is the solution to the initial–boundary value problem, is observed at a single boundary point over a finite time interval. Based on the expansion of eigenfunctions for the solution to the forward problem and the asymptotic properties of the Mittag-Leffler function, the uniqueness of the fractional order is established. Subsequently, the uniqueness of the eigenvalues and the absolute value of the eigenfunction evaluated at <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span> for the associated operator are demonstrated. Then, the uniqueness of identifying the diffusion coefficient and the Robin coefficient is proven via an inverse boundary spectral analysis for the eigenvalue problem of the spatial differential operator. The results show that the uniqueness of three parameters can be simultaneously determined using limited boundary observations at a single spatial endpoint over a finite time interval, without imposing any constraints on the eigenfunctions of the spatial differential operator.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109386"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109381
Juan Gerardo Alcázar , Michal Bizzarri , Miroslav Lávička , Jan Vršek
We prove that, under generic conditions, the covariance matrix of a 3D point cloud with rotational symmetry has a simple eigenvalue, whose associated eigenvector provides the direction of the axis of rotation, and a double eigenvalue. The direction of the axis of rotation can also be computed from higher order tensors related to the point cloud, which is useful in pathological cases. This leads to a very simple algorithm for detecting rotational symmetry and computing the axis of rotation.
{"title":"Rotational symmetries of 3D point clouds using the covariance matrix and higher-order tensors","authors":"Juan Gerardo Alcázar , Michal Bizzarri , Miroslav Lávička , Jan Vršek","doi":"10.1016/j.aml.2024.109381","DOIUrl":"10.1016/j.aml.2024.109381","url":null,"abstract":"<div><div>We prove that, under generic conditions, the covariance matrix of a 3D point cloud with rotational symmetry has a simple eigenvalue, whose associated eigenvector provides the direction of the axis of rotation, and a double eigenvalue. The direction of the axis of rotation can also be computed from higher order tensors related to the point cloud, which is useful in pathological cases. This leads to a very simple algorithm for detecting rotational symmetry and computing the axis of rotation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109381"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109387
Fiona McIntosh, Lily Amirzadeh, Brian E. Moore
Explicit, conformal symplectic, exponential time differencing (ETD) methods have numerous advantages over other well-known and commonly used methods, including structure-preservation, high stability, ease of implementation, and computational efficiency. Such methods are constructed with second and fourth order accuracy through composition techniques using a simple first order scheme. For modeling Josephson Junctions, these ETD schemes regularly exhibit the best balance of efficiency and accuracy when compared to other commonly used methods.
{"title":"Structure-preserving exponential time differencing methods for modeling Josephson Junctions","authors":"Fiona McIntosh, Lily Amirzadeh, Brian E. Moore","doi":"10.1016/j.aml.2024.109387","DOIUrl":"10.1016/j.aml.2024.109387","url":null,"abstract":"<div><div>Explicit, conformal symplectic, exponential time differencing (ETD) methods have numerous advantages over other well-known and commonly used methods, including structure-preservation, high stability, ease of implementation, and computational efficiency. Such methods are constructed with second and fourth order accuracy through composition techniques using a simple first order scheme. For modeling Josephson Junctions, these ETD schemes regularly exhibit the best balance of efficiency and accuracy when compared to other commonly used methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109387"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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