共查询到20条相似文献,搜索用时 78 毫秒
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将不等距离分割方法与人工鱼群算法相结合,提出一种基于人工鱼群算法求任意函数数值积分的方法,该方法除能计算通常意义下任意函数的定积分外,还能计算奇异函数积分、振荡函数积分以及原函数不易求得的被积函数的积分.最后给出几个数值积分算例,并与传统数值积分方法作了比较,仿真结果分析表明,该算法十分有效,能够快速有效地获得任意函数的数值积分值. 相似文献
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In this paper, a numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection diffusion equation is presented. The convergence and stability of the numerical approximation method are discussed by a new technique of Fourier analysis. The solvability of the numerical approximation method also is analyzed. Finally, applying Richardson extrapolation technique, a high-accuracy algorithm is structured and the numerical example demonstrated the theoretical results. 相似文献
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In this article, a numerical method for recovering the local volatility in Black–Scholes model is proposed based on the Dupire formula in which the numerical derivatives are used. By Tikhonov regularization, a new numerical differentiation method in two-dimensional (2-D) case is presented. The convergent analysis and numerical examples are also given. It shows that our method is efficient and stable. 相似文献
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《Journal of Computational and Applied Mathematics》2012,236(2):209-224
In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis. 相似文献
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Chang-Ming ChenF. Liu K. Burrage 《Journal of Computational and Applied Mathematics》2011,236(2):209-224
In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis. 相似文献
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Elçin Yusufo?lu 《Applied mathematics and computation》2010,217(7):3591-3595
A numerical method for solving the generalized (retarded or advanced) pantograph equation under initial value conditions is presented. To display the validity and applicability of the numerical method four illustrative examples are presented. The results reveal that this method is very effective and highly promising when compared with other numerical methods, such as Adomian decomposition method, spline methods and Taylor method. 相似文献
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In this paper, we consider an anomalous subdiffusion process, governed by fractional Fokker-Planck equation. An effective numerical method for approximating Fokker-Planck equation in a bounded domain is presented. The stability and convergence of the numerical method are analyzed. Some numerical examples are presented to show the application of the present technique. The numerical results exhibit the good performance of our theoretical analysis. 相似文献
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DGH方程作为一类重要的非线性水波方程有着许多广泛的应用前景.基于Hamilton系统的多辛理论研究了一类强色散DGH方程的数值解法,利用多辛普雷斯曼方法构造了一种典型的半隐式的多辛格式.分析了该格式的局部能量和动量守恒律误差,并给出了数值算例.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性. 相似文献
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A semi‐discrete defect correction finite element method for unsteady incompressible magnetohydrodynamics equations
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In this report, we give a semi‐discrete defect correction finite element method for the unsteady incompressible magnetohydrodynamics equations. The defect correction method is an iterative improvement technique for increasing the accuracy of a numerical solution without applying a grid refinement. Firstly, the nonlinear magnetohydrodynamics equations is solved with an artificial viscosity term. Then, the numerical solutions are improved on the same grid by a linearized defect‐correction technique. Then, we give the numerical analysis including stability analysis and error analysis. The numerical analysis proves that our method is stable and has an optimal convergence rate. In order to show the effect of our method, some numerical results are shown. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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对流扩散方程的一种显式有限体积——有限元方法 总被引:4,自引:0,他引:4
窦红 《应用数学与计算数学学报》2001,15(2):45-52
本文给出非线性对流扩散问题的一种有限体积的有限元方法相结合的显式离散方法,证明了数值解的稳定性,并给出了一个实际算例。 相似文献
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本文主要研究了线性随机分数阶微分方程Euler方法的弱收敛性与弱稳定性.首先构造了数值求解线性随机分数阶微分方程的Euler方法,然后证明该方法是弱稳定的和α阶弱收敛的,文末给出的数值算例验证了所获得的理论结果的正确性. 相似文献
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A fast numerical verification method is proposed for evaluating the accuracy of numerical solutions for symmetric saddle point linear systems whose diagonal blocks of the coefficient matrix are semidefinite matrices. The method is based on results of an algebraic analysis of a block diagonal preconditioning. Some numerical experiments are present to illustrate the usefulness of the method. 相似文献
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A numerical perturbation expansion method is developed, analysed and implemented for the numerical solution of a second-order initial-value problem. The differential equation in this problem exhibits cubic damping, a cubic restoring force and a decaying forcing-term which is periodic with constant frequency. The method is compared with the numerical method by Twizell [1]. In fact, the later is first perturbation approximate solution in the present paper. 相似文献
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K.-A. Lie V. Haugse K. Hvistendahl Karlsen 《Numerical Methods for Partial Differential Equations》1998,14(5):627-648
Front tracking in combination with dimensional splitting is analyzed as a numerical method for scalar conservation laws in two space dimensions. An analytic error bound is derived, and convergence rates based on numerical experiments are presented. Numerical experiments indicate that large CFL numbers can be used without loss of accuracy for a wide range of problems. A new method for grid refinement is introduced. The method easily allows for dynamical changes in the grid, using, for instance, the total variation in each grid cell as a criterion for introducing new or removing existing refinements. Several numerical examples are included, highlighting the features of the numerical method. A comparison with a high-resolution method confirms that dimensional splitting with front tracking is a highly viable numerical method for practical computations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 627–648, 1998 相似文献
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The operator splitting method is a widely used approach for solving partial differential equations describing physical processes. Its application usually requires the use of certain numerical methods in order to solve the different split sub-problems. The error analysis of such a numerical approach is a complex task. In the present paper we show that an interaction error appears in the numerical solution when an operator splitting procedure is applied together with a lower-order numerical method. The effect of the interaction error is investigated by an analytical study and by numerical experiments made for a test problem. 相似文献
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Mohamed El-Gamel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,26(1):369-383
A numerical technique for solving time-dependent problems with variable coefficient governed by the heat, convection diffusion,
wave, beam and telegraph equations is presented. The Sinc–Galerkin method is applied to construct the numerical solution.
The method is tested on three problems and comparisons are made with the exact solutions. The numerical results demonstrate
the reliability and efficiency of using the Sinc–Galerkin method to solve such problems. 相似文献
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N.I. Ioakimidis 《Applied mathematics and computation》1983,12(1):49-60
The collocation method for the numerical solution of Fredholm integral equations of the second kind is applied, properly modified, to the numerical solution of Cauchy type singular integral equations of the first or the second kind but with constant coefficients. This direct method of numerical solution of Cauchy type singular integral equations is compared afterwards with the corresponding method resulting from applying the collocation method to the Fredholm integral equation of the second kind equivalent to the Cauchy type singular integral equation, as well as with another method, based also on the regularization procedure, for the numerical solution of the same class of equations. Finally, the convergence of the method is discussed. 相似文献