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Numerical Methods for Partial Differential Equations最新文献

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A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model 亚扩散模型下分数 Black-Scholes 方程的小波配位法
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-05-02 DOI: 10.1002/num.23103
Davood Damircheli, Mohsen Razzaghi
{"title":"A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model","authors":"Davood Damircheli, Mohsen Razzaghi","doi":"10.1002/num.23103","DOIUrl":"https://doi.org/10.1002/num.23103","url":null,"abstract":"In this investigation, we propose a numerical method based on the fractional‐order generalized Taylor wavelets (FGTW) for option pricing and the fractional Black–Scholes equations. This model studies option pricing when the underlying asset has subdiffusive dynamics. By applying the regularized beta function, we give an exact formula for the Riemann–Liouville fractional integral operator (RLFIO) of the FGTW. An error analysis of the numerical scheme for estimating solutions is performed. Finally, we conduct a variety of numerical experiments for several standard examples from the literature to assess the efficiency of the proposed method.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"45 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Error estimates for completely discrete FEM in energy‐type and weaker norms 能量型和弱规范下完全离散有限元的误差估计
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-05-02 DOI: 10.1002/num.23106
Lutz Angermann, Peter Knabner, Andreas Rupp
{"title":"Error estimates for completely discrete FEM in energy‐type and weaker norms","authors":"Lutz Angermann, Peter Knabner, Andreas Rupp","doi":"10.1002/num.23106","DOIUrl":"https://doi.org/10.1002/num.23106","url":null,"abstract":"The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion‐convection‐reaction equations and boundary conditions of mixed type. Since neither conformity nor consistency properties are assumed, the method is called completely discrete. We investigate two different stabilized discretizations and obtain stability and optimal error estimates in energy‐type norms and, by generalizing the Aubin‐Nitsche technique, optimal error estimates in weaker norms.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"3 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind 二维弱奇异 Volterra 第二类积分方程的广义对数正交函数谱配位法
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-04-29 DOI: 10.1002/num.23105
Qiumei Huang, Min Wang
{"title":"Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind","authors":"Qiumei Huang, Min Wang","doi":"10.1002/num.23105","DOIUrl":"https://doi.org/10.1002/num.23105","url":null,"abstract":"In this article, a generalized log orthogonal functions (GLOFs)‐spectral collocation method to two dimensional weakly singular Volterra integral equations of the second kind is proposed. The mild singularities of the solution at the interval endpoint can be captured by Gauss‐GLOFs quadrature and the shortcoming of the traditional spectral method which cannot well deal with weakly singular Volterra integral equations with limited regular solutions is avoided. A detailed convergence analysis of the numerical solution is carried out. The efficiency of the proposed method is demonstrated by numerical examples.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"82 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Primal‐dual active set algorithm for valuating American options under regime switching 制度转换下美式期权估值的原始二元有源集算法
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-04-18 DOI: 10.1002/num.23104
Haiming Song, Jingbo Xu, Jinda Yang, Yutian Li
{"title":"Primal‐dual active set algorithm for valuating American options under regime switching","authors":"Haiming Song, Jingbo Xu, Jinda Yang, Yutian Li","doi":"10.1002/num.23104","DOIUrl":"https://doi.org/10.1002/num.23104","url":null,"abstract":"This paper focuses on numerical algorithms to value American options under regime switching. The prices of such options satisfy a set of complementary parabolic problems on an unbounded domain. Based on our previous experience, the pricing model could be truncated into a linear complementarity problem (LCP) over a bounded domain. In addition, we transform the resulting LCP into an equivalent variational problem (VP), and discretize the VP by an Euler‐finite element method. Since the variational matrix in the discretized system is P‐matrix, a primal‐dual active set (PDAS) algorithm is proposed to evaluate the option prices efficiently. As a specialty of PDAS, the optimal exercise boundaries in all regimes are obtained without further computation cost. Finally, numerical simulations are carried out to test the performance of our proposed algorithm and compare it to existing methods.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"2014 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unconditional H2$$ {H}^2 $$‐stability of the Euler implicit/explicit SAV‐based scheme for the 2D Navier–Stokes equations with smooth or nonsmooth initial data 具有光滑或非光滑初始数据的二维纳维-斯托克斯方程基于欧拉隐式/显式 SAV 方案的无条件 H2$$ {H}^2 $$ 稳定性
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-03-27 DOI: 10.1002/num.23099
Teng‐Yuan Chang, Ming‐Cheng Shiue
{"title":"Unconditional H2$$ {H}^2 $$‐stability of the Euler implicit/explicit SAV‐based scheme for the 2D Navier–Stokes equations with smooth or nonsmooth initial data","authors":"Teng‐Yuan Chang, Ming‐Cheng Shiue","doi":"10.1002/num.23099","DOIUrl":"https://doi.org/10.1002/num.23099","url":null,"abstract":"In this article, we propose ‐unconditional stable schemes for solving time‐dependent incompressible Navier–Stokes equations with smooth or nonsmooth initial data, , . The ‐stability analysis is established by leveraging the scalar auxiliary variable (SAV) approach. When dealing with nonsmooth initial data, we utilize a limited number of iteration of the semi‐implicit scheme followed by the SAV scheme. The overall efficiency is greatly enhanced due to the minimal computational cost of the semi‐implicit scheme and the explicit treatment of the nonlinear term within the SAV approach. The proposed schemes investigate two types of scalar auxiliary variables: the energy‐based variable and the exponential‐based variable. Rigorous proofs of the ‐unconditional stability of both schemes have been provided. Notice that both proposed numerical schemes enjoy unconditional long time stability for smooth and nonsmooth initial data when . Numerical experiments have been conducted to demonstrate the theoretical results.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"48 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A posteriori error estimate of the weak Galerkin finite element method solving the Stokes problems on polytopal meshes 弱 Galerkin 有限元方法解决多桌面网格上斯托克斯问题的后验误差估计
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-03-27 DOI: 10.1002/num.23102
Shipeng Xu
{"title":"A posteriori error estimate of the weak Galerkin finite element method solving the Stokes problems on polytopal meshes","authors":"Shipeng Xu","doi":"10.1002/num.23102","DOIUrl":"https://doi.org/10.1002/num.23102","url":null,"abstract":"In this paper, we propose an a posteriori error estimate of the weak Galerkin finite element method (WG-FEM) solving the Stokes problems with variable coefficients. Its error estimator, based on the property of Stokes' law conservation, Helmholtz decomposition and bubble functions, yields global upper bound and local lower bound for the approximation error of the WG-FEM. Error analysis is proved to be valid under the mesh assumptions of the WG-FEM and the way can be extended to other FEMs with the property of Stokes' law conservation, for example, discontinuous Galerkin (DG) FEMs. Finally, we verify the performance of error estimator by performing a few numerical examples.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"7 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140325209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An a posteriori error analysis for an augmented discontinuous Galerkin method applied to Stokes problem 应用于斯托克斯问题的增强非连续伽勒金方法的后验误差分析
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-03-23 DOI: 10.1002/num.23100
Tomás P. Barrios, Rommel Bustinza
{"title":"An a posteriori error analysis for an augmented discontinuous Galerkin method applied to Stokes problem","authors":"Tomás P. Barrios, Rommel Bustinza","doi":"10.1002/num.23100","DOIUrl":"https://doi.org/10.1002/num.23100","url":null,"abstract":"This paper deals with the a posteriori error analysis for an augmented mixed discontinuous formulation for the stationary Stokes problem. By considering an appropriate auxiliary problem, we derive an a posteriori error estimator. We prove that this estimator is reliable and locally efficient, and consists of just five residual terms. Numerical experiments confirm the theoretical properties of the augmented discontinuous scheme as well as of the estimator. They also show the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"74 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations 不可压缩斯托克斯方程解耦方法中可局部计算的 P3 压力
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-03-22 DOI: 10.1002/num.23101
Chunjae Park
{"title":"A locally calculable P3‐pressure in a decoupled method for incompressible Stokes equations","authors":"Chunjae Park","doi":"10.1002/num.23101","DOIUrl":"https://doi.org/10.1002/num.23101","url":null,"abstract":"This article will suggest a new finite element method to find a ‐velocity and a ‐pressure solving incompressible Stokes equations at low cost. The method solves first the decoupled equation for a ‐velocity. Then, using the calculated velocity, a locally calculable ‐pressure will be defined component‐wisely. The resulting ‐pressure is analyzed to have the optimal order of convergence. Since the pressure is calculated by local computation only, the chief time cost of the new method is on solving the decoupled equation for the ‐velocity. Besides, the method overcomes the problem of singular vertices or corners.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"2015 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow 平流-扩散-反应布林克曼流混合有限元法的新最佳误差分析
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-03-16 DOI: 10.1002/num.23097
Huadong Gao, Wen Xie
{"title":"A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow","authors":"Huadong Gao, Wen Xie","doi":"10.1002/num.23097","DOIUrl":"https://doi.org/10.1002/num.23097","url":null,"abstract":"This article deals with the error analysis of a Galerkin‐mixed finite element methods for the advection–reaction–diffusion Brinkman flow in porous media. Numerical methods for incompressible miscible flow in porous media have been studied extensively in the last several decades. In practical applications, the lowest‐order Galerkin‐mixed method is the most popular one, where the linear Lagrange element is used for the concentration and the lowest‐order Raviart–Thomas element, the lowest‐order Nédélec edge element and piece‐wise constant discontinuous Galerkin element are used for the velocity, vorticity and pressure, respectively. The existing error estimate of this lowest‐order finite element method is only for all variables in spatial direction, which is not optimal for the concentration variable. This paper focuses on a new and optimal error estimate of a linearized backward Euler Galerkin‐mixed FEMs, where the second‐order accuracy for the concentration in spatial directions is established unconditionally. The key to our optimal error analysis is a new negative norm estimate for Nédélec edge element. Moreover, based on the computed numerical concentration, we propose a simple one‐step recovery technique to obtain a new numerical velocity, vorticity and pressure with second‐order accuracy. Numerical experiments are provided to confirm our theoretical analysis.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"118 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations 磁流体力学方程全压力隔离方案的无条件最优一阶误差估计
IF 3.9 3区 数学
Numerical Methods for Partial Differential Equations Pub Date : 2024-03-16 DOI: 10.1002/num.23098
Yun‐Bo Yang, Yao‐Lin Jiang
{"title":"Unconditional optimal first‐order error estimates of a full pressure segregation scheme for the magnetohydrodynamics equations","authors":"Yun‐Bo Yang, Yao‐Lin Jiang","doi":"10.1002/num.23098","DOIUrl":"https://doi.org/10.1002/num.23098","url":null,"abstract":"In this article, a first‐order linear fully discrete pressure segregation scheme is studied for the time‐dependent incompressible magnetohydrodynamics (MHD) equations in three‐dimensional bounded domain. Based on an incremental pressure projection method, this scheme allows us to decouple the MHD system into two sub‐problems at each time step, one is the velocity‐magnetic field system, the other is the pressure system. Firstly, a coupled linear elliptic system is solved for the velocity and the magnetic field. Next, a Poisson‐Neumann problem is treated for the pressure. We analyze the temporal error and the spatial error, respectively, and derive the temporal‐spatial error estimates of for the velocity and the magnetic field in the discrete space and for the pressure in the discrete space without imposing constraints on the mesh width and the time step size . Finally, some numerical results are presented to confirm the theoretical predictions and demonstrate the efficiency of the method.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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