共查询到20条相似文献,搜索用时 781 毫秒
1.
高凌云 《数学年刊A辑(中文版)》2014,35(2):193-202
研究了具有允许的亚纯解的复差分方程的形式以及系数的级与解的级两者的关系,得到了两个结果.将复微分方程中一些结果推广至复差分方程. 相似文献
2.
In this paper we introduce a new type of explicit numerical algorithm to solve the spatially discretized linear heat or diffusion equation. After discretizing the space variables as in standard finite difference methods, this novel method does not approximate the time derivatives by finite differences, but use three stage constant-neighbor and linear neighbor approximations to decouple the ordinary differential equations and solve them analytically. In the final expression for the new values of the variable, the time step size appears not in polynomial or rational, but in exponential form with negative coefficients, which can guarantee unconditional stability. The scheme contains a free parameter p. We show that the convergence of the method is third-order in the time step size regardless of the values of p, and, according to von Neumann stability analysis, the method is stable for a wide range of p. We validate the new method by testing the results in a case where the analytical solution exists, then we demonstrate the competitiveness by comparing its performance with several other numerical solvers. 相似文献
3.
We introduce an orthogonal system on the half line, induced by Jacobi polynomials. Some results on the Jacobi rational approximation are established, which play important roles in designing and analyzing the Jacobi rational spectral method for various differential equations, with the coefficients degenerating at certain points and growing up at infinity. The Jacobi rational spectral method is proposed for a model problem appearing frequently in finance. Its convergence is proved. Numerical results demonstrate the efficiency of this new approach.
4.
Martin Bohner 《Journal of Difference Equations and Applications》2013,19(6):767-792
We consider first and second order linear dynamic equations on a time scale. Such equations contain as special cases differential equations, difference equationsq— difference equations, and others. Important properties of the exponential function for a time scale are presented, and we use them to derive solutions of first and second order linear dyamic equations with constant coefficients. Wronskians are used to study equations with non—constant coefficients. We consider the reduction of order method as well as the method of variation of constants for the nonhomogeneous case. Finally, we use the exponential function to present solutions of the Euler—Cauchy dynamic equation on a time scale. 相似文献
5.
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative coefficients). We propose to consider a class of methods that allows us to evaluate all time-dependent operators at real values of the time, leading to schemes which are stable and simple to implement. If the system can be considered as the perturbation of an exactly solvable problem and the flow of the dominant part is advanced using real coefficients, it is possible to build highly efficient methods for these problems. We show the performance of this class of methods on several numerical examples and present some new improved schemes. 相似文献
6.
M.A. Abdou S.S. Abd ElGawad 《Numerical Methods for Partial Differential Equations》2010,26(6):1608-1623
An extended mapping method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for nonlinear evolution equations arising in physics, namely, generalized Zakharov Kuznetsov equation with variable coefficients. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations with variable coefficients arising in mathematical physics. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
7.
J. Rubió-Massegú 《Journal of Mathematical Analysis and Applications》2008,343(1):182-189
A new necessary condition for global periodicity of discrete dynamical systems and of difference equations is obtained here. This condition will be applied to contribute to solving the problem of global periodicity for second order rational difference equations. 相似文献
8.
Nan Li 《Journal of Difference Equations and Applications》2013,19(2):237-250
In this paper, we investigate the complex oscillation problems of meromorphic solutions to some linear difference equations with meromorphic coefficients, and obtain some results about the relationships between the exponent of convergence of zeros, poles and the order of growth of meromorphic solutions to complex linear difference equations. We also study the existence of solution of certain types of nonlinear differential-difference equations, and partially answer a conjecture concerning the above problem posed by Yang and Laine (C.C. Yang and I. Laine, On analogies between nonlinear difference and differential equations, Proc. Japan Acad. Ser. A Math. Sci. 86(1) (2010), pp. 10–14). 相似文献
9.
Frobenius integrable decompositions are presented for a kind of ninth-order partial differential equations of specific polynomial type. Two classes of such partial differential equations possessing Frobenius integrable decompositions are connected with two rational Bäcklund transformations of dependent variables. The presented partial differential equations are of constant coefficients, and the corresponding Frobenius integrable ordinary differential equations possess higher-order nonlinearity. The proposed method can be also easily extended to the study of partial differential equations with variable coefficients. 相似文献
10.
Guo Chun Wen 《数学学报(英文版)》2011,27(10):2051-2064
The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate
hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations
is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of
solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point principle.
In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions
in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order
equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients,
and then the advantage of complex analytic method can be applied. 相似文献
11.
Jiří Gregor 《Acta Appl Math》1998,53(3):247-263
We want to discuss partial difference equations, first of all with respect to the existence and uniqueness of their solution. These equations are considered with solutions on arbitrary subsets of the n-dimensional grid Zn. The basic theorem enables one to formulate the Cauchy problem for such equations. The solution is proven to be recursively computable for partial difference equations under very mild restrictions. (Variable coefficients for linear equations, systems of equations as well as nonlinear equations are not excluded.) The construction of solutions presented here also allows for some qualitative conclusions, such as boundedness of solutions. 相似文献
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13.
Jun Wang 《Journal of Mathematical Analysis and Applications》2011,379(1):367-377
This paper is devoted to studying the growth property and the pole distribution of meromorphic solutions f of some complex difference equations with all coefficients being rational functions or of growth S(r,f). We find the lower bound of the lower order, or the relation between lower order and the convergence exponent of poles of meromorphic solutions of such equations. 相似文献
14.
Diego Dominici 《Journal of Difference Equations and Applications》2018,24(6):916-940
We derive a system of difference equations satisfied by the three-term recurrence coefficients of some families of discrete orthogonal polynomials. 相似文献
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16.
Steven B. Bank 《Applicable analysis》2013,92(3-4):209-233
In this paper we obtain new results on the location of complex Zeros of soulutions of linear differential equations of arbitrary order whose coofficients are rational funcitons. 相似文献
17.
Douglas R. Anderson 《Journal of Mathematical Analysis and Applications》2011,373(2):709-725
We study non-self-adjoint Hamiltonian systems on Sturmian time scales, defining Weyl-Sims sets, which replace the classical Weyl circles, and a matrix-valued M-function on suitable cone-shaped domains in the complex plane. Furthermore, we characterize realizations of the corresponding dynamic operator and its adjoint, and construct their resolvents. Even-order scalar equations and the Orr-Sommerfeld equation on time scales are given as examples illustrating the theory, which are new even for difference equations. These results unify previous discrete and continuous theories to dynamic equations on Sturmian time scales. 相似文献
18.
In this paper we provide a version of the Floquet’s theorem to be applied to any second order difference equations with quasi-periodic coefficients. To do this we extend to second order linear difference equations with quasi-periodic coefficients, the known equivalence between the Chebyshev equations and the second order linear difference equations with constant coefficients. So, any second order linear difference equations with quasi-periodic coefficients is essentially equivalent to a Chebyshev equation, whose parameter only depends on the values of the quasi-periodic coefficients and can be determined by a non-linear recurrence. Moreover, we solve this recurrence and obtaining a closed expression for this parameter. As a by-product we also obtain a Floquet’s type result; that is, the necessary and sufficient condition for the equation has quasi-periodic solutions. 相似文献
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20.
Artur M. Ishkhanyan 《Journal of Applied Analysis & Computation》2019,9(1):118-139
We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The approach employs an auxiliary equation involving only the derivatives of a solution of the equation under consideration. Using power-series expansions of the solutions of this auxiliary equation, we construct several expansions of the four confluent Heun equations'' solutions in terms of the incomplete Gamma-functions. In the cases of single- and double-confluent Heun equations the coefficients of the expansions obey four-term recurrence relations, while for the bi- and tri-confluent Heun equations the recurrence relations in general involve five terms. Other expansions for which the expansion coefficients obey recurrence relations involving more terms are also possible. The particular cases when these relations reduce to ones involving less number of terms are identified. The conditions for deriving closed-form finite-sum solutions via right-hand side termination of the constructed series are discussed. 相似文献