共查询到20条相似文献,搜索用时 906 毫秒
1.
Martin Gugat Günter Leugering Alexander Martin Martin Schmidt Mathias Sirvent David Wintergerst 《Computational Optimization and Applications》2018,70(1):267-294
We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network. 相似文献
2.
A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk’s second-order rational, and van Niekerk’s third-order rational methods are presented. 相似文献
3.
构造了两维Chaplygin气体Euler方程组的三参数、自相似的弱解.在自相似和轴对称的假设下,两维Chaplygin气体Euler方程组可以化为无穷远边值的常微分方程组,由此得到了解的存在性和解的结构.与多方气体不同的是Chaplygin气体的Euler方程组是完全线性退化的.即使在轴向速度大于零的时候解也会出现间断现象.这些解展示了宇宙演化过程中的一些现象,例如黑洞的形成与演化以及宇宙的暴涨和膨胀. 相似文献
4.
Large time asymptotics of compressible Euler equations for a polytropic gas with and without the porous media equation are constructed in which the Barenblatt solution is embedded. Invariance analysis for these governing equations are carried out using the classical and the direct methods. A new second order nonlinear partial differential equation is derived and is shown to reduce to an Euler–Painlevé equation. A regular perturbation solution of a reduced ordinary differential equation is determined. And an exact closed form solution of a system of ordinary differential equations is derived using the invariance analysis. 相似文献
5.
《Journal of Computational and Applied Mathematics》2006,185(2):422-440
Stochastic differential equations (SDEs) models play a prominent role in many application areas including biology, epidemiology and population dynamics, mostly because they can offer a more sophisticated insight through physical phenomena than their deterministic counterparts do. So, suitable numerical methods must be introduced to simulate the solutions of the resulting stochastic differential systems. In this work we take into account both Euler–Taylor expansion and Runge–Kutta-type methods for stochastic ordinary differential equations (SODEs) and the Euler–Maruyama method for stochastic delay differential equations (SDDEs), focusing on the most relevant implementation issues. The corresponding Matlab codes for both SODEs and SDDEs problems are tested on mathematical models arising in the biosciences. 相似文献
6.
V. P. Derevenskii 《Mathematical Notes》2008,84(3-4):342-355
In this paper, we determine the coefficients of left-side linear ordinary differential equations with constant coefficients over a noncommutative Banach algebra; these equations have solutions of Euler type. 相似文献
7.
Hossein Aminikhah Jafar Biazar 《Numerical Methods for Partial Differential Equations》2010,26(2):480-489
In this paper, we introduce a new version of the homotopy perturbation method (NHPM) that efficiently solves linear and non‐linear ordinary differential equations. Several examples, including Euler‐Lagrange, Bernoulli and Ricatti differential equations, are given to demonstrate the efficiency of the new method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
8.
Natalija Tumanova Raimondas Čiegis Mečislavas Meilūnas 《Central European Journal of Mathematics》2013,11(6):1140-1152
This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented. 相似文献
9.
Dimitrios E. PanayotounakosIoanna Rizou Efstathios E. Theotokoglou 《Applied mathematics and computation》2011,217(21):8534-8542
It is shown that the three nonlinear dynamic Euler ordinary differential equations (ODEs), concerning the motion of a rigid body free to rotate about a fixed point, are reduced, by means of a subsidiary function which is to be determined, to three Abel equations of the second kind of the normal form. Based on a recently developed mathematical construction concerning exact analytic solutions of the Abel nonlinear ODEs of the second kind, we perform a new mathematical solution for the classical dynamic Euler nonlinear ODEs. 相似文献
10.
Eisenmann Monika Kovács Mihály Kruse Raphael Larsson Stig 《Foundations of Computational Mathematics》2019,19(6):1387-1430
Foundations of Computational Mathematics - In this paper, we introduce a randomized version of the backward Euler method that is applicable to stiff ordinary differential equations and nonlinear... 相似文献
11.
12.
Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the numerical method of lines are given. An explicit Euler method is proposed for the numerical solution of systems thus obtained. This leads to difference scheme for the original problem. A complete convergence analysis for the method is given. 相似文献
13.
Numerical Algorithms - We analyse errors of randomized explicit and implicit Euler schemes for approximate solving of ordinary differential equations (ODEs). We consider classes of ODEs for which... 相似文献
14.
V. F. Chistyakov 《Numerical Analysis and Applications》2011,4(4):363-375
Implicit methods applied to the numerical solution of systems of ordinary differential equations (ODEs) with an identically singular matrix multiplying the derivative of the sought-for vector-function are considered. The effects produced by losing L-stability of a classical implicit Euler scheme when solving such stiff systems are discussed. 相似文献
15.
Toshiyuki Koto 《Frontiers of Mathematics in China》2009,4(1):113-129
Stability properties of implicit-explicit (IMEX) linear multistep methods for ordinary and delay differential equations are
analyzed on the basis of stability regions defined by using scalar test equations. The analysis is closely related to the
stability analysis of the standard linear multistep methods for delay differential equations. A new second-order IMEX method
which has approximately the same stability region as that of the IMEX Euler method, the simplest IMEX method of order 1, is
proposed. Some numerical results are also presented which show superiority of the new method.
相似文献
16.
Euler integral transformations relate solutions of ordinary linear differential equations and generate integral representations
of the solutions in a number of cases or relations between solutions of constrained equations (Euler symmetries) in some other
cases. These relations lead to the corresponding symmetries of the monodromy matrices. We discuss Euler symmetries in the
case of the simplest Fuchsian system that is equivalent to a deformed Heun equation, which is in turn related to the Painlevé
PVI equation. The existence of integral symmetries of the deformed Heun equation leads to the corresponding symmetries of
the PVI equation.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 252–264, May, 2008. 相似文献
17.
Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV
Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or relations between solutions of constrained equations. These relations lead to the corresponding symmetries of the monodromy matrices for the differential equations. We discuss Euler symmetries in the case of the deformed confluent Heun equation, which is in turn related to the Painlevé equation PV. The existence of symmetries of the linear equations leads to the corresponding symmetries of the Painlevé equation of the Okamoto type. The choice of the system of linear equations that reduces to the deformed confluent Heun equation is the starting point for the constructions. The basic technical problem is to choose the bijective relation between the system parameters and the parameters of the deformed confluent Heun equation. The solution of this problem is quite large, and we use the algebraic computing system Maple for this. 相似文献
18.
S.B Engelsman 《Historia Mathematica》1980,7(1):7-23
In 1776, J. L. Lagrange gave a definition of the concept of a “complete solution” of a first-order partial differential equation. This definition was entirely different from the one given earlier by Euler. One of the sources for Lagrange's reformulation of this concept can be found in his attempt to explain the occurrence of singular solutions of ordinary differential equations. Another source of the new definition is contained in an earlier treatise of Lagrange [1774] in which he elaborated an approach to first-order partial differential equations briefly indicated by Euler. The method of “variation of constants,” which was fundamental to his argument, suggested to Lagrange the reformulation of the concept of a “complete solution.” In the present paper I shall discuss both sources of the new definition of “completeness.” 相似文献
19.
Sueet Millon Sahoo T. Raja Sekhar G. P. Raja Sekhar 《Mathematical Methods in the Applied Sciences》2020,43(9):5744-5757
We derive exact solutions of one-dimensional Euler system that accounts for gravity together with large friction. Certain optimal classes of subalgebra using Lie symmetry analysis are obtained for this system. We apply the reduction procedure to reduce the Euler system to a system of ordinary differential equations in terms of new similarity variable for each class of subalgebras leading to invariant solutions. The evolution of characteristic shock and its interaction with the weak discontinuity by using one of the invariant solutions is studied. Further, the properties of reflected and transmitted waves and jump in acceleration influenced by the incident wave have been characterized. 相似文献
20.
E. H. Twizell Yigong Wang W. G. Price F. Fakhr 《Numerical Methods for Partial Differential Equations》1994,10(4):435-454
Numerical methods are proposed for the numerical solution of a system of reaction-diffusion equations, which model chemical wave propagation. The reaction terms in this system of partial differential equations contain nonlinear expressions. Nevertheless, it is seen that the numerical solution is obtained by solving a linear algebraic system at each time step, as opposed to solving a nonlinear algebraic system, which is often required when integrating nonlinear partial differential equations. The development of each numerical method is made in the light of experience gained in solving the system of ordinary differential equations, which model the well-stirred analogue of the chemical system. The first-order numerical methods proposed for the solution of this initialvalue problem are characterized to be implicit. However, in each case it is seen that the numerical solution is obtained explicitly. In a series of numerical experiments, in which the ordinary differential equations are solved first of all, it is seen that the proposed methods have superior stability properties to those of the well-known, first-order, Euler method to which they are compared. Incorporating the proposed methods into the numerical solution of the partial differential equations is seen to lead to two economical and reliable methods, one sequential and one parallel, for solving the travelling-wave problem. © 1994 John Wiley & Sons, Inc. 相似文献