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Numerical Solution of Conformable Stochastic Differential Equations Driven by Fractional Brownian Motion 认领 引用
1
作者 CHEN Yinmeng XIA Xiaoyu YAN Litan 《应用数学》 北大核心 2026年第3期880-886,共7页
This paper investigates numerical solutions for stochastic fractional differential equations driven by fractional Brownian motion.We develop an approximation scheme for the fractional noise term and establish a corres... This paper investigates numerical solutions for stochastic fractional differential equations driven by fractional Brownian motion.We develop an approximation scheme for the fractional noise term and establish a corresponding numerical method.The theoretical analysis includes proving the stability of the numerical solution and its convergence to the exact solution.Numerical experiments implement the Jacobi method to simulate a conformable stochastic differential equation,demonstrating the method's performance through solution behavior and error distribution analysis. 展开更多
关键词 Stochastic fractional differential equation Fractional Brownian motion Numerical solution Jacobi spectral Galerkin method
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Introduction to the Special Issue on Analytical and Numerical Solution of the Fractional Differential Equation 认领 引用
2
作者 Ndolane Sene Ameth Ndiaye 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第12期2849-2852,共4页
Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its u... Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions. 展开更多
关键词 mathematical physical sciences numerical solutions fractional diffusion equationsin fractional operators fractional differential equations analytical solutions intelligent artificial systemsamong
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Efficient Numerical Solution of the Modified Mild-Slope Equation 认领 引用 被引量：15
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作者 潘军宁 左其华 王红川 《China Ocean Engineering》 SCIE EI 2000年第2期161-174,共14页
An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an im... An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced. 展开更多
关键词 wave mild-slope equation numerical solution stability refraction diffraction reflection
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Numerical Solutions of a New Type of Fractional Coupled Nonlinear Equations 认领 引用 被引量：4
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作者 CHEN Yong AN Hong-Li 《Communications in Theoretical Physics》 SCIE CAS 2008年第4期839-844,共6页
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo＇s definition, we directly extend the applications of the Adomian ... In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo＇s definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples： KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method. 展开更多
关键词 Adomian decomposition method fractional calculus fractional coupled equations numerical solution
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Numerical solutions to heat transfer of nanofluid flow over stretching sheet subjected to variations of nanoparticle volume fraction and wall temperature 认领 引用 被引量：2
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作者 M.SALARI M.MOHAMMADTABAR A.MOHAMMADTABAR 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第1期63-72,共10页
The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise va... The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers. 展开更多
关键词 stretching sheet nanofluid laminar boundary layer Brownian motion,thermophoresis partial differential equation numerical solution
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Numerical solution of a mathematical model for water wavesin large coastal areas 认领 引用
6
作者 Zheng Yonghong Shen Yongming Xia Jin 《Acta Oceanologica Sinica》 SCIE CAS 2000年第4期17-23,共7页
Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. T... Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort. 展开更多
关键词 Water wave mathematical model numerical solution
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Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: Numerical Solution 认领 引用
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作者 Noreen Sher Akbar Zafar Hayat Khan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第6期681-687,共7页
In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transfo... In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically. 展开更多
关键词 two-dimensional flow variable nanofluid viscosity stagnation-point flow stretching sheet carbon nanotubes numerical solution
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Governing equations and numerical solutions of tension leg platform with finite amplitude motion 认领 引用
8
作者 曾晓辉 沈晓鹏 吴应湘 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第1期37-49,共13页
It is demonstrated that when tension leg platform （TLP） moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP,... It is demonstrated that when tension leg platform （TLP） moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP, The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theo- retical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displace- ment, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force, Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP. 展开更多
关键词 tension leg platform （TLP）, finite displacement nonlinear dynamic response, numerical solution, wave loads
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Approximate Formulation and Numerical Solution for Hypersingular Boundary Integral Equations in Plane Elasticity 认领 引用
9
作者 马杭 黄兴 《Journal of Shanghai University(English Edition)》 2003年第2期124-130,共7页
Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general app... Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations. 展开更多
关键词 hypersingular boundary integral equation numerical solution approximate formulation splitting distance.
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NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM FOR THE HYPERBOLIC EQUATION WITH INITIAL JUMP 认领 引用
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作者 苏煜城 林平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第8期709-721,共13页
In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constru... In this paper we consider the initial-boundary value problem for a second order hyperbolic equation with initial jump. The bounds on the derivatives of the exact solution are given. Then a difference scheme is constructed on a non-uniform grid. Finally, uniform convergence of the difference solution is proved in the sense of the discrete energy norm. 展开更多
关键词 NUMERICAL SOLUTION OF THE SINGULARLY PERTURBED PROBLEM FOR THE HYPERBOLIC EQUATION WITH INITIAL JUMP
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NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS 认领 引用
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作者 林平 苏煜城 《Applied Mathematics and Mechanics(English Edition)》 SCIE 1989年第11期1005-1010,共6页
In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an alg... In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 . 展开更多
关键词 NUMERICAL SOLUTION OF QUASILINEAR SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITHOUT TURNING POINTS
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Numerical Solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law 认领 引用
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作者 Qiang DU Zhan HUANG 《Journal of Mathematical Research with Applications》 CSCD 2017年第1期1-18,共18页
In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enj... In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local conservation laws in the form of partial differential equations. We discuss convergent numerical approximations that preserve similar properties on the discrete level.We also present numerical experiments to study various limiting behavior of the numerical solutions. 展开更多
关键词 nonlocal model nonlinear hyperbolic conservation laws maximum principle monotonicity preserving numerical solution
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Numerical Solutions of a Class of Nonlinear Evolution Equations with Nonlinear Term of Any Order 认领 引用 被引量：2
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作者 AN Hong-Li CHEN Yong 《Communications in Theoretical Physics》 SCIE CAS 2008年第3期579-584,共6页
In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contain... In this paper, the Adomian decomposition method is developed for the numerical solutions of a class of nonlinear evolution equations with nonlinear term of any order, utt＋auxx ＋ bu ＋ cu^p＋ du^2p-1=0, which contains some important famous equations. When setting the initial conditions in different forms, some new generalized numerical solutions： numerical hyperbolic solutions, numerical doubly periodic solutions are obtained. The numerical solutions are compared with exact solutions. The scheme is tested by choosing different values of p, positive and negative, integer and fraction, to illustrate the efficiency of the ADM method and the generalization of the solutions. 展开更多
关键词 Adomian decomposition method nonlinear evolution equations Jacobi elliptic function numerical solution
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NUMERICAL SOLUTIONS OF DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR GENERAL ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER 认领 引用 被引量：2
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作者 黄沙 闻国椿 《Acta Mathematica Scientia》 SCIE 2000年第2期162-168,共7页
In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary... In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions. 展开更多
关键词 elliptic complex equations numerical solutions boundary value problem
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Existence and Numerical Solution for a Coupled System of Multi-term Fractional Differential Equations 认领 引用 被引量：1
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作者 杨李凡 叶海平 《Journal of Donghua University(English Edition)》 EI CAS 2015年第4期613-619,共7页
An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the ex... An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results. 展开更多
关键词 multi-term fractional differential equation Caputo derivative existence uniqueness numerical solution
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ON THE NUMERICAL SOLUTION OF QUASILINEAR WAVE EQUATION WITH STRONG DISSIPATIVE TERM 认领 引用 被引量：2
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作者 Aytekin Gülle 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第7期806-811,共6页
The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The... The numerical solution for a type of quasilinear wave equation is studied.The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved.The error of the difference solution is estimated.The theoretical results are controlled on a numerical example. 展开更多
关键词 periodical problem quasilinear wave equation difference scheme numerical solution
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ON NUMERICAL SOLUTIONS OF PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS 认领 引用
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作者 刘国庆 傅冬生 沈祖和 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第2期226-235,共10页
A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the unif... A nonlinear perturbed conservative system is discussed. BY means of Hadamard's theorem. the existence and uniqueness of the solution of the continuous problem arc proved. When the equation is discreted on the uniform meshes, it is proved that the corresponding discrete problem has a unique solution, Finally, the accuracy of the numerical solution is considered and a simple algorithm is provided for solving the nonlinear difference equation. 展开更多
关键词 nonlinear system numerical solution uniqueness and existence algorithm
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Numerical Solution of the Weight Function for Electromagnetic Flowmeter 认领 引用 被引量：4
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作者 FAN Shi-wei CAO Zhang +1 位作者 XU Li-jun WANG Gang 《Computer Aided Drafting,Design and Manufacturing》 2010年第2期36-41,共6页
A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-ele... A numerical solution of the weight function for a two-electrode electromagnetic flowmeter was proposed. The solution was obtained by using the finite element method based on the basic equation of a traditional two-electrode electromagnetic flowmeter. The two-dimensional distribution of the weight function of the electromagnetic flowmeter obtained was verified by the analytical solution. Three-dimensional distribution of the weight function was also presented in the paper. It can be employed to analyze the sensitivity and linearity of the electromagnetic flowmeter with non-uniform magnetic field, and even to assist the design of the excitation coil pair. 展开更多
关键词 electromagnetic flowmeter weight function finite element method numerical solution virtual current
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Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics 认领 引用 被引量：2
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作者 R.G. Muharliamov 《应用数学》 北大核心 2001年第2期103-119,共17页
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant... In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined. 展开更多
关键词 Kinematies Dynamical equations Constraints Lagrange’s equations Rigid body Numerical solution Differential algebraic equations
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Numerical Solution for Fractional Partial Differential Equation with Bernstein Polynomials 认领 引用
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作者 Jin-Sheng Wang Li-Qing Liu +1 位作者 Yi-Ming Chen Xiao-Hong Ke 《Journal of Electronic Science and Technology》 CAS 2014年第3期331-338,共8页
A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational ma... A framework to obtain numerical solution of the fractional partial differential equation using Bernstein polynomials is presented. The main characteristic behind this approach is that a fractional order operational matrix of Bernstein polynomials is derived. With the operational matrix, the equation is transformed into the products of several dependent matrixes which can also be regarded as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient. 展开更多
关键词 Absolute error Bernstein polynomials fractional partial differential equation numerical solution operational matrix
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