共查询到20条相似文献,搜索用时 15 毫秒
1.
Moulay A. Barkatou Gary Broughton Eckhard Pflügel 《Mathematics in Computer Science》2010,4(2-3):267-288
This paper deals with the local analysis of systems of pseudo-linear equations. We define regular solutions and use this as a unifying theoretical framework for discussing the structure and existence of regular solutions of various systems of linear functional equations. We then give a generic and flexible algorithm for the computation of a basis of regular solutions. We have implemented this algorithm in the computer algebra system Maple in order to provide novel functionality for solving systems of linear differential, difference and q-difference equations given in various input formats. 相似文献
2.
Summary This paper discusses the problems associated with the symbolic treatment of functional equations and presents a Mathematica
package for the solution of real functional equations of real variables. The package includes a minimal basic database which
contains a reduced set of functional equations with its four components: equation, domain, class and the corresponding solution.
The word minimal is used in the sense that any equation that is solvable by the system using non-searching methods is excluded
from the database. The package incorporates a searching algorithm which can solve functional equations independently of their
notation and their algebraic representation. Not only general solutions but particular and candidate solutions are dealt with.
This implies a careful analysis of domains and classes. The package includes some methods for solving functional equations,
which are used when the input functional equations are not found in the database. Some methods have been implemented internally
and some are in an external package. Finally, some examples illustrate the use of the package. 相似文献
3.
Om P. Agrawal 《Journal of Mathematical Analysis and Applications》2008,337(1):1-12
This paper presents a general finite element formulation for a class of Fractional Variational Problems (FVPs). The fractional derivative is defined in the Riemann-Liouville sense. For FVPs the Euler-Lagrange and the transversality conditions are developed. In the Fractional Finite Element Formulation (FFEF) presented here, the domain of the equations is divided into several elements, and the functional is approximated in terms of nodal variables. Minimization of this functional leads to a set of algebraic equations which are solved using a numerical scheme. Three examples are considered to show the performance of the algorithm. Results show that as the number of discretization is increased, the numerical solutions approach the analytical solutions, and as the order of the derivative approaches an integer value, the solution for the integer order system is recovered. For unspecified boundary conditions, the numerical solutions satisfy the transversality conditions. This indicates that for the class of problems considered, the numerical solutions can be obtained directly from the functional, and there is no need to solve the fractional Euler-Lagrange equations. Thus, the formulation extends the traditional finite element approach to FVPs. 相似文献
4.
We present a non-periodic averaging principle for measure functional differential equations and, using the correspondence between solutions of measure functional differential equations and solutions of functional dynamic equations on time scales (see Federson et al., 2012 [8]), we obtain a non-periodic averaging result for functional dynamic equations on time scales. Moreover, using the relation between measure functional differential equations and impulsive measure functional differential equations, we get a non-periodic averaging theorem for these equations. Also, it is a known fact that we can relate impulsive measure functional differential equations and impulsive functional dynamic equations on time scales (see Federson et al., 2013 [9]). Therefore, applying this correspondence to our averaging principle, we obtain a non-periodic averaging theorem for impulsive functional dynamic equations on time scales. 相似文献
5.
Yu. N. Kudrya 《Theoretical and Mathematical Physics》1995,102(1):87-97
A theorem giving the necessary and sufficient conditions for Penrose's exact sets of spinor fields in curved spacetimes is proved. An algorithm for augmenting a system of fields to an exact set and constructing covariant Taylor expansions for the fields of an exact set is proposed. The general approach is applied to test massive spin 3/2 fields. Two possible forms of exact sets are constructed for them on the basis of modified Dirac-Fierz-Pauli equations. The functional arbitrariness in the solutions of the equations for exact sets is determined. In one of the cases, the obtained exact set can be interpreted as a system of fields of spins 3/2 and 1/2 interacting through the gravitational field.State University, Kiev. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 1, pp. 119–133, January, 1995. 相似文献
6.
In this paper we propose a new algebraic algorithm to compute the exact travelling wave solutions of nonlinear differential–difference equations. The idea of the proposed algorithm is generated from generalizing the hyperbolic cotangent (coth-) function. Numerical examples are given to illustrate the efficiency and effectiveness of the proposed method. It has been shown that new types of exact travelling wave solutions for these nonlinear differential–difference equations can be constructed. 相似文献
7.
The purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes. By using fixed point theorems, a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established. Under certain conditions, some existence theorems of coincidence solutions for the class of system of functional equations are shown. Some examples are given to demonstrate the advantage of our results than existing ones in the literature. 相似文献
8.
Piotr Zgliczynski 《Foundations of Computational Mathematics》2008,2(4):429-465
Abstract. We present a modification of the Lohner algorithm for the computation of rigorous bounds for solutions of ordinary differential
equations together with partial derivatives with respect to initial conditions. The modified algorithm requires essentially
the same computational effort as the original one. We applied the algorithm to show the existence of several periodic orbits
for R?ssler equations and the 14-dimensional Galerkin projection of the Kuramoto—Sivashinsky partial differential equation. 相似文献
9.
Fourier series and Taylor's expansions are commonly used in the fields of science and engineering. A whole range of interesting physical problems can be solved using one or the other of these standard techniques. Yet, there is a class of problems whose solutions exhibit near sinusoidal or repetitive behavior that cannot be solved using the above expansions. It is for these types of problems that the modified Taylor expansion has been developed. It is a method that combines the advantages of the repetitive behavior of sinusoidal functions and polynomial series. This technique has not been employed for tackling equations whose solutions are near sinusoidal. We discuss the method and apply it to a number of interesting problems that show its utility. Examples include the solution of differential, integral, integro-differential and functional equations. In addition, we propose an algorithm for the numerical integration of a function which exhibits near periodic behavior, namely the Bessel function. Most of the symbolic and numerical computations have been performed using the Computer Algebra System––Maple. 相似文献
10.
11.
把最近提出的G′/G展开法推广到了非线性微分差分方程,利用该方法成功构造了一种修正的Volterra链和Toda链的双曲函数、三角函数以及有理函数三类涉及任意参数的行波解,当这些参数取特殊值时,可得这两个方程的扭状孤立波解、奇异行波解以及三角函数状的周期波解等.研究结果表明,该算法探讨非线性微分差分方程精确解十分有效、简洁. 相似文献
12.
Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid. We use an algorithm of Contejean and Devie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. and Comput. 113 (1994) 143-172] to show how these presentations can be obtained from the nonnegative integer solutions to a linear system of equations. We later introduce an alternate algorithm to show how such a presentation can be efficiently computed from an integer basis. 相似文献
13.
We introduce the concept of a generalized conditional symmetry. This concept provides an algorithm for constructing physically important exact solutions of non-integrable equations. Examples include 2-shock and 2-soliton solutions. The existence of such exact solutions for non-integrable equations can be traced back to the relation of these equations with integrable ones. In this sense these exact solutions are remnants of integrability.Department of Mathematics and Computer Science and Institute for Nonlinear Studies, Clarkson University, Potsdam, New York 13699-5815. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 263–277, May, 1994. 相似文献
14.
Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise 下载免费PDF全文
In this paper, we consider the non‐Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non‐Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
15.
In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa-Holm equation, Kolmogorov-Petrovskii-Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the (2+1)-dimensional asymmetric version of the Nizhnik-Novikov-Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems. 相似文献
16.
E. V. Trifonov 《Theoretical and Mathematical Physics》2017,192(1):974-981
We propose a procedure for multiplying solutions of linear and nonlinear one-dimensional wave equations, where the speed of sound can be an arbitrary function of one variable. We obtain exact solutions. We show that the functional series comprising these solutions can be used to solve initial boundary value problems. For this, we introduce a special scalar product. 相似文献
17.
该文基于一个Riccati方程组,提出了一个新的广义投影Ric cati展开法,该方法直接简单并能构造非线性微分方程更多的新的解析解。利用该算法研究了(2+1)维广义浅水波方程,并求得了许多新的精确解,包括类孤子解和周期解。该算法也能应用到其它非线性微分方程中。 相似文献
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19.
《Mathematical Methods in the Applied Sciences》2018,41(7):2664-2672
In the present paper, exact solutions of fractional nonlinear Schrödinger equations have been derived by using two methods: Lie group analysis and invariant subspace method via Riemann‐Liouvill derivative. In the sense of Lie point symmetry analysis method, all of the symmetries of the Schrödinger equations are obtained, and these operators are applied to find corresponding solutions. In one case, we show that Schrödinger equation can be reduced to an equation that is related to the Erdelyi‐Kober functional derivative. The invariant subspace method for constructing exact solutions is presented for considered equations. 相似文献
20.
In 1999, Christopher gave a necessary and sufficient condition for polynomial Li′enard centers, which requires coupled functional equations, where the primitive functions of the damping function and the restoring function are involved, to have polynomial solutions. In order to judge whether the coupled functional equations are solvable, in this paper we give an algorithm to compute a Gr¨obner basis for irreducible decomposition of algebraic varieties so as to find algebraic relations among coefficients of the damping function and the restoring function. We demonstrate the algorithm for polynomial Li′enard systems of degree 5, which are divided into 25 cases. We find all conditions of those coefficients for the polynomial Li′enard center in 13 cases and prove that the origin is not a center in the other 12 cases. 相似文献