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Continuous-Time Channel Prediction Based on Tensor Neural Ordinary Differential Equation
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作者 Mingyao Cui Hao Jiang +2 位作者 Yuhao Chen Yang Du Linglong Dai 《China Communications》 SCIE CSCD 2024年第1期163-174,共12页
Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channe... Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channel in a fixed time slot per frame,while the other intra-frame channels are usually recovered by interpolation.However,these approaches suffer from a serious interpolation loss,especially for mobile millimeter-wave communications.To solve this challenging problem,we propose a tensor neural ordinary differential equation(TN-ODE)based continuous-time channel prediction scheme to realize the direct prediction of intra-frame channels.Specifically,inspired by the recently developed continuous mapping model named neural ODE in the field of machine learning,we first utilize the neural ODE model to predict future continuous-time channels.To improve the channel prediction accuracy and reduce computational complexity,we then propose the TN-ODE scheme to learn the structural characteristics of the high-dimensional channel by low-dimensional learnable transform.Simulation results show that the proposed scheme is able to achieve higher intra-frame channel prediction accuracy than existing schemes. 展开更多
关键词 channel prediction massive multipleinput-multiple-output millimeter-wave communications ordinary differential equation
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New Numerical Integration Formulations for Ordinary Differential Equations
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作者 Serdar Beji 《Advances in Pure Mathematics》 2024年第8期650-666,共17页
An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions ... An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations. 展开更多
关键词 Single- and Multi-Step Numerical Integration Unconventional Base-Functions ordinary differential equations
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Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method
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作者 Mariam Al-Mazmumy Aishah A. Alsulami 《Journal of Applied Mathematics and Physics》 2023年第1期85-100,共16页
This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an... This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of. 展开更多
关键词 Modification Method Singular ordinary differential equations Laguerre’s equation Associated Laguerre’s equation
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New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions 被引量:15
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作者 段文洋 戴遗山 《China Ocean Engineering》 SCIE EI 2001年第4期499-508,共9页
Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D G... Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics. 展开更多
关键词 marine hydrodynamics TIME-DOMAIN Green function ordinary differential equation Laplace transform
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HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS 被引量:4
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作者 Wang Tongke(王同科) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第2期213-225,共13页
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me... In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective. 展开更多
关键词 SECOND order ordinary differential equation TWO-POINT boundary value problem high accuracy finite volume element method error estimate.
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On Exact Solutions of Second Order Nonlinear Ordinary Differential Equations 被引量:3
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作者 Amjed Zraiqat Laith K. Al-Hwawcha 《Applied Mathematics》 2015年第6期953-957,共5页
In this paper, a new approach for solving the second order nonlinear ordinary differential equation y’’ + p(x;y)y’ = G(x;y) is considered. The results obtained by this approach are illustrated by examples and show ... In this paper, a new approach for solving the second order nonlinear ordinary differential equation y’’ + p(x;y)y’ = G(x;y) is considered. The results obtained by this approach are illustrated by examples and show that this method is powerful for this type of equations. 展开更多
关键词 Nonlinear ordinary differential equation PARTIAL differential equation RICCATI differential equation
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ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS 被引量:3
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作者 张汉林 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第5期471-480,共10页
In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and t... In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated. 展开更多
关键词 REAL ON THE SINGULAR PERTURBATION OF A NONLINEAR ordinary differential equation WITH TWO PARAMETERS exp
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A New Circulant Preconditioned GMRES Method for Solving Ordinary Differential Equation 被引量:1
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作者 朱睦正 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期535-544,共10页
The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value... The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric,large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods.In this paper,we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method, which is a convex linear combination of P-circulant and Strang-type circulant preconditioners. Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases. 展开更多
关键词 circulant preconditioner boundary value method ordinary differential equation(ODE) GMRES
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A Novel Method for Solving Ordinary Differential Equations with Artificial Neural Networks 被引量:3
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作者 Roseline N. Okereke Olaniyi S. Maliki Ben I. Oruh 《Applied Mathematics》 2021年第10期900-918,共19页
This research work investigates the use of Artificial Neural Network (ANN) based on models for solving first and second order linear constant coefficient ordinary differential equations with initial conditions. In par... This research work investigates the use of Artificial Neural Network (ANN) based on models for solving first and second order linear constant coefficient ordinary differential equations with initial conditions. In particular, we employ a feed-forward Multilayer Perceptron Neural Network (MLPNN), but bypass the standard back-propagation algorithm for updating the intrinsic weights. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial or boundary conditions and contains no adjustable parameters. The second part involves a feed-forward neural network to be trained to satisfy the differential equation. Numerous works have appeared in recent times regarding the solution of differential equations using ANN, however majority of these employed a single hidden layer perceptron model, incorporating a back-propagation algorithm for weight updation. For the homogeneous case, we assume a solution in exponential form and compute a polynomial approximation using statistical regression. From here we pick the unknown coefficients as the weights from input layer to hidden layer of the associated neural network trial solution. To get the weights from hidden layer to the output layer, we form algebraic equations incorporating the default sign of the differential equations. We then apply the Gaussian Radial Basis function (GRBF) approximation model to achieve our objective. The weights obtained in this manner need not be adjusted. We proceed to develop a Neural Network algorithm using MathCAD software, which enables us to slightly adjust the intrinsic biases. We compare the convergence and the accuracy of our results with analytic solutions, as well as well-known numerical methods and obtain satisfactory results for our example ODE problems. 展开更多
关键词 ordinary differential equations Multilayer Perceptron Neural Networks Gaussian Radial Basis Function Network Training MathCAD (Computer Aided Design) 14 IBM-SPSS (Statistical Package for Social Science) 23
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On Trigonometric Numerical Integrator for Solving First Order Ordinary Differential Equation 被引量:1
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作者 A. A. Obayomi S. O. Ayinde O. M. Ogunmiloro 《Journal of Applied Mathematics and Physics》 2019年第11期2564-2578,共15页
In this paper, we used an interpolation function with strong trigonometric components to derive a numerical integrator that can be used for solving first order initial value problems in ordinary differential equation.... In this paper, we used an interpolation function with strong trigonometric components to derive a numerical integrator that can be used for solving first order initial value problems in ordinary differential equation. This numerical integrator has been tested for desirable qualities like stability, convergence and consistency. The discrete models have been used for a numerical experiment which makes us conclude that the schemes are suitable for the solution of first order ordinary differential equation. 展开更多
关键词 NUMERICAL INTEGRATOR ordinary differential equation INITIAL Value Problems Stability Analysis NONSTANDARD METHODS INTERPOLATION METHODS
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PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS 被引量:1
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作者 A. Bensebah F. Dubeau J. Gelinas 《Analysis in Theory and Applications》 1997年第3期78-90,共13页
A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th... A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given. 展开更多
关键词 PROJECTION METHODS AND APPROXIMATIONS FOR ordinary differential equationS ODE
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An Adaptive Time-Step Backward Differentiation Algorithm to Solve Stiff Ordinary Differential Equations: Application to Solve Activated Sludge Models 被引量:2
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作者 Jamal Alikhani Bahareh Shoghli +1 位作者 Ujjal Kumar Bhowmik Arash Massoudieh 《American Journal of Computational Mathematics》 2016年第4期298-312,共15页
A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency ... A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters. 展开更多
关键词 Adaptive Time-Step Backward differentiation Formula Activated Sludge Model ordinary differential equation Stiffness Computation Time
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A ONE-STEP EXPLICIT FORMULA FOR THE NUMERICAL SOLUTION OF STIFF ORDINARY DIFFERENTIAL EQUATION
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作者 吴新元 夏建林 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1999年第1期53-58,共6页
In this paper, a new one-step explicit method of fourth order is derived. The new method is proved to be A-stable and L-stable, and it gives exact results when applied to the test equation y’=λy with Re(λ)【0, Also... In this paper, a new one-step explicit method of fourth order is derived. The new method is proved to be A-stable and L-stable, and it gives exact results when applied to the test equation y’=λy with Re(λ)【0, Also several numerical examples are included. 展开更多
关键词 STIFF equation NUMERICAL stability NUMERICAL solutions of ordinary differential equation NUMERICAL analysis.
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DIFFERENTIATOR SERIES SOLUTION OF LINEAR DIFFERENTIAL ORDINARY EQUATION
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作者 柯红路 谢和熙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第8期59-66,共8页
In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential d... In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge. 展开更多
关键词 linear ordinary differential equation differentiator series method special solution general solution
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On Bifurcations of an Ordinary Differential Equation
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作者 LI Chang-pin College of Sciences, Shanghai University, Shanghai 200436, China 《Advances in Manufacturing》 SCIE CAS 2000年第S1期4-6,共3页
Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization r... Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization results. 展开更多
关键词 BIFURCATIONS ordinary differential equation singularity theory Liapunov-Schlnidt reduction
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ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH TURNING POINTS
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作者 JIANG Fu-ru(江福汝) +1 位作者 JIN Qi-nian(金其年) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第4期394-403,共10页
Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) ... Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained. 展开更多
关键词 boundary value problems ordinary differential equations turning points asymptotic solutions
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NUMERICAL SOLUTION OF NONLINEAR ORDINARY DIFFERENTIAL EQUATION FOR A TURNING POINT PROBLEM
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作者 林鹏程 白清源 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第11期1055-1065,共11页
By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained. With the help o... By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained. With the help of the technique in [4], the uniform convergence on the small parameter e for a difference scheme is proved. At the end of this paper, a numerical example is given. The numerical result coincides with theoretical analysis. 展开更多
关键词 nonlinear ordinary differential equation turning point singular perturbation problem difference scheme uniform convergence
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THE ESTIMATION OF SOLUTION OF THE BOUNDARY VALUE PROBLEM OF THE SYSTEMS FOR QUASI-LINEAR ORDINARY DIFFERENTIAL EQUATIONS
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作者 黄蔚章 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第8期745-754,共10页
This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix ... This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder. 展开更多
关键词 systems of the quasi-linear ordinary differential equation singular perturbation DIAGONALIZATION asymptotic expansion
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ON THE BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH TURNING POINTS
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作者 江福汝 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第2期121-129,共9页
In this paper, we consider the boundary value problems of the form ey″ - f(x, e)y′ + g(x, e)y=0 (-a&lex&leb, 0<e1) y(-a)=a, y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The ... In this paper, we consider the boundary value problems of the form ey″ - f(x, e)y′ + g(x, e)y=0 (-a&lex&leb, 0<e1) y(-a)=a, y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed. 展开更多
关键词 ordinary differential equations singular perturbation turning point problem
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Hojman's theorem of the third-order ordinary differential equation
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作者 吕洪升 张宏彬 顾书龙 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第8期3135-3138,共4页
This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The gener... This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results. 展开更多
关键词 third-order ordinary differential equation Lie symmetry Hojman's conservation law
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