共查询到19条相似文献,搜索用时 234 毫秒
1.
2.
3.
4.
本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法.对于给定的的代数方城组,通过正规分解,可以得到一组具有三角形式的分解.根据这种三角形式,我们可以给出代数方程组的所有解.而对于带有参数方程组,将给出方程组有解时参数需满足的条件.进一步,对于给定的参数值,正规分解中得到三角形式仍然保持,通过求解三角形式的方程组从而得出原参数方程组的解. 相似文献
5.
针对m阶非线性Volterra-Fredholm型积分微分方程,利用勒让德-伽辽金方法进行求解.勒让德多项式被选作基函数,通过基函数与残差正交得到有限维方程组,求解有限维方程组得到待定系数,便能求出方程的近似解.一些数值算例的给出证明了方法的可行性和有效性. 相似文献
6.
基于Jacobi正交多项式法,直接求解一般形式的对偶积分方程组,将对偶积分方程组中的未知函数,表示成n次Jacobi正交多项式级数,用正交多项式将奇异对偶积分方程组,化成线性代数方程组,通过求解级数中的各项系数,由此给出奇异对偶积分方程组的一般性解,并严格证明了奇异对偶积分方程组和由它化成的线性代数方程组的等价性,解的存在性和解的表示形式不唯一性.本文给出的理论解和解法,可供求解复杂的数学、物理、软科学中的混合边值问题应用. 相似文献
7.
8.
以浅水长波近似方程组为例,提出了拟小波方法求解(1 1)维非线性偏微分方程组数值解,该方程用拟小波离散格式离散空间导数,得到关于时间的常微分方程组,用四阶Runge-K utta方法离散时间导数,并将其拟小波解与解析解进行比较和验证. 相似文献
9.
10.
阻尼Gauss-Newton方法解非线性不等式组 总被引:1,自引:1,他引:0
本文研究了非线性不等式组的求解问题.利用了阻尼Gauss-Newton方法求解非线性方程组,获得了该算法的全局收敛性,推广了Gauss-Newton法在解非线性方程组方面的应用. 相似文献
11.
Computational bounds on polynomial differential equations 总被引:1,自引:0,他引:1
Daniel S. Graça Jorge Buescu Manuel L. Campagnolo 《Applied mathematics and computation》2009,215(4):1375-1385
In this paper we study from a computational perspective some properties of the solutions of polynomial ordinary differential equations.We consider elementary (in the sense of Analysis) discrete-time dynamical systems satisfying certain criteria of robustness. We show that those systems can be simulated with elementary and robust continuous-time dynamical systems which can be expanded into fully polynomial ordinary differential equations in Q[π]. This sets a computational lower bound on polynomial ODEs since the former class is large enough to include the dynamics of arbitrary Turing machines.We also apply the previous methods to show that the problem of determining whether the maximal interval of definition of an initial-value problem defined with polynomial ODEs is bounded or not is in general undecidable, even if the parameters of the system are computable and comparable and if the degree of the corresponding polynomial is at most 56.Combined with earlier results on the computability of solutions of polynomial ODEs, one can conclude that there is from a computational point of view a close connection between these systems and Turing machines. 相似文献
12.
Conditional Lie‐Bäcklund symmetry (CLBS) method is developed to study system of evolution equations. It is shown that reducibility of a system of evolution equations to a system of ordinary differential equations can be fully characterized by the CLBS of the considered system. As an application of the approach, a class of two‐component nonlinear diffusion equations is studied. The governing system and the admitted CLBS can be identified. As a consequence, exact solutions defined on the polynomial, exponential, trigonometric, and mixed invariant subspaces are constructed due to the corresponding symmetry reductions. 相似文献
13.
Summary A method to generate an accurate approximation to a singular solution of a system of complex analytic equations is presented. Since manyreal systems extend naturally tocomplex analytic systems, this porvides a method for generating approximations to singular solutions to real systems. Examples include systems of polynomials and systems made up of trigonometric, exponential, and polynomial terms. The theorem on which the method is based is proven using results from several complex variables. No special conditions on the derivatives of the system, such as restrictions on the rank of the Jacobian matrix at the solution, are required. The numerical method itself is developed from techniques of homotopy continuation and 1-dimensional quadrature. A specific implementation is given, and the results of numerical experiments in solving five test problems are presented. 相似文献
14.
15.
Adnan Al-Smadi 《International Journal of Mathematical Education in Science & Technology》2013,44(5):743-753
In theory, there are many methods for the representation of signals. In practice, however, Fourier analysis involving the resolution of signals into sinusoidal components is used widely. There are several methods for Fourier analysis available for representation of signals. If the signal is periodic, then the Fourier series is used to represent the signal in terms of a set of harmonically related sinewaves. In this article new formulae for evaluating the trigonometric Fourier series coefficients when the signal under consideration is polynomial are developed by changing the integration to a derivation form. The solution presented here is an extension of the formulae proposed by Al-Smadi and Wilkes to the trigonometric Fourier series. The proposed technique is a powerful tool that can be used for solving practical science and engineering problems without excessive tedium. 相似文献
16.
Hoang Si Nguyen Roger B. Sidje Nguyen Huu Cong 《Journal of Computational and Applied Mathematics》2007
Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge–Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge–Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. 相似文献
17.
Recently, the class of Hamiltonian Boundary Value Methods (HBVMs) has been introduced with the aim of preserving the energy associated with polynomial Hamiltonian systems (and, more in general, with all suitably regular Hamiltonian systems). However, many interesting problems admit other invariants besides the Hamiltonian function. It would be therefore useful to have methods able to preserve any number of independent invariants. This goal is achieved by generalizing the line-integral approach which HBVMs rely on, thus obtaining a number of generalizations which we collectively name Line Integral Methods. In fact, it turns out that this approach is quite general, so that it can be applied to any numerical method whose discrete solution can be suitably associated with a polynomial, such as a collocation method, as well as to any conservative problem. In particular, a completely conservative variant of both HBVMs and Gauss collocation methods is presented. Numerical experiments confirm the effectiveness of the proposed methods. 相似文献
18.
Shaukat Iqbal 《Numerical Methods for Partial Differential Equations》2011,27(6):1551-1560
In this article, a Galerkin's finite element approach based on weighted‐residual is presented to find approximate solutions of a system of fourth‐order boundary‐value problems associated with obstacle, unilateral and contact problems. The approach utilizes a piece‐wise cubic approximations utilizing cubic Hermite interpolation polynomials. Numerical studies have shown the superior accuracy and lesser computational cost of the scheme in comparison to cubic spline, non‐polynomial spline and cubic non‐polynomial spline methods. Numerical examples are presented to illustrate the applicability of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1551–1560, 2011 相似文献
19.
Probability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that, under mild assumptions, are globally convergent for a wide range of problems in science and engineering. Convergence theory, robust numerical algorithms, and production quality mathematical software exist for general nonlinear systems of equations, and special cases such as Brouwer fixed point problems, polynomial systems, and nonlinear constrained optimization. Using a sample of challenging scientific problems as motivation, some pertinent homotopy theory and algorithms are presented. The problems considered are analog circuit simulation (for nonlinear systems), reconfigurable space trusses (for polynomial systems), and fuel-optimal orbital rendezvous (for nonlinear constrained optimization). The mathematical software packages HOMPACK90 and POLSYS_PLP are also briefly described. 相似文献