共查询到19条相似文献,搜索用时 118 毫秒
1.
Identifying the temperature distribution in a parabolice quation with overspecified data using a multiquadric quasi-interpolation method 下载免费PDF全文
In this paper, we use a kind of univariate multiquadric
quasi-interpolation to solve a parabolic equation with overspecified
data, which has arisen in many physical phenomena. We obtain the
numerical scheme by using the derivative of the quasi-interpolation
to approximate the spatial derivative of the dependent variable and
a simple forward difference to approximate the temporal derivative
of the dependent variable. The advantage of the presented scheme is
that the algorithm is very simple so it is very easy to
implement. The results of the numerical experiment are presented and are
compared with the exact solution to confirm the good accuracy of the
presented scheme. 相似文献
2.
A meshless scheme for partial differential equations based on multiquadric trigonometric B-spline quasi-interpolation 下载免费PDF全文
Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into ac- count the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the dif- ficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions. 相似文献
3.
The computational criteria used to judge the correctness of numerical calculation for sound propagationin ducts are presented.An improved finite-difference scheme is also obtained to solve the problem with thediscontinuity in the wall impedance.Moreover,a set of curves of numerical solutions compared withexperimental results for sound propagation in a practical hard-soft-hard wall duct and other samples arealso presented.The results show that the criteria and approach to discontinuity are successful and thatcomputational model is suitable. 相似文献
4.
Pradip Roul 《理论物理通讯》2013,(9)
The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial difusion of biological populations.The homotopy–perturbation method is employed for solving this class of equations,and the time-fractional derivatives are described in the sense of Caputo.Comparisons are made with those derived by Adomian’s decomposition method,revealing that the homotopy perturbation method is more accurate and convenient than the Adomian’s decomposition method.Furthermore,the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efcient technique for solving the fractional diferential equations without requiring linearization or restrictive assumptions.The basis ideas presented in the paper can be further applied to solve other similar fractional partial diferential equations. 相似文献
5.
In this paper, we derive a new method for a nonlinear Schrodinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ||·||2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws. 相似文献
6.
A local refinement purely meshless scheme for time fractional nonlinear Schrodinger equation in irregular geometry region 下载免费PDF全文
A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross-Pitaevskii equation(TF-GPE)with the rotating Bose-Einstein condensate.It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge.The proposed LRCSPH-FDM(which is based on a local refinement corrected SPH method combined with FDM)is derived by using the finite difference scheme(FDM)to discretize the Caputo TF term,followed by using a corrected smoothed particle hydrodynamics(CSPH)scheme continuously without using the kernel derivative to approximate the spatial derivatives.Meanwhile,the local refinement technique is adopted to reduce the numerical error.In numerical simulations,the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method.The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D(where 1D stands for one-dimensional)analytical TF-NLSEs in a rectangular region(with regular or irregular particle distribution)or in a region with irregular geometry.The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain,and the results from the posed method are compared with those from the FDM.All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape. 相似文献
7.
The idea of the present article is to look into the nonlinear dynamics and vibration of a damping Duffing-jerk oscillator in fractal space exhibiting the non-perturbative approach. Using a new analytical technique, namely, the modification of a He’s fractal derivative that converts the fractal derivative to the traditional derivative in continuous space, this study provides an effective and easy-to-apply procedure that is dependent on the He’s fractal derivative approach.The analytic approximate... 相似文献
8.
WANG Xian-Jun FU Jing-Li 《理论物理通讯》2008,50(11):1041-1046
This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results. 相似文献
9.
Approximate solution for the Klein-Gordon-SchrSdinger equation by the homotopy analysis method 下载免费PDF全文
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution. 相似文献
10.
Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method 下载免费PDF全文
The Homotopy analysis method is applied to obtain the approximate solution of the Klein--Gordon--Schr?dinger equation. The Homotopy analysis solutions of the Klein--Gordon--Schr?dinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution. 相似文献
11.
In this study, we present a new and very accurate numerical method to approximate the Fisher’s-type equations. Firstly, the
spatial derivative in the proposed equation is approximated by a sixth-order compact finite difference (CFD6) scheme. Secondly,
we solve the obtained system of differential equations using a third-order total variation diminishing Runge–Kutta (TVD-RK3)
scheme. Numerical examples are given to illustrate the efficiency of the proposed method. 相似文献
12.
Pierre-Henri Maire 《Journal of computational physics》2009,228(7):2391-2425
We present a high-order cell-centered Lagrangian scheme for solving the two-dimensional gas dynamics equations on unstructured meshes. A node-based discretization of the numerical fluxes for the physical conservation laws allows to derive a scheme that is compatible with the geometric conservation law (GCL). Fluxes are computed using a nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The first-order scheme is conservative for momentum and total energy, and satisfies a local entropy inequality in its semi-discrete form. The two-dimensional high-order extension is constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess this new scheme. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new scheme. 相似文献
13.
Jerzy Stanek 《Central European Journal of Physics》2011,9(6):1503-1508
Applying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of the screening parameter. The results are compared with those obtained by the other approximate and numerical methods. It is shown that the present method is systematic, more efficient and accurate. 相似文献
14.
给出抛物方程一种有效的区域分裂差分格式,提高了计算效率.对一阶项采用二阶迎风差分格式,内边界点和各子区域分别采用显隐差分格式.在较弱的稳定性条件下,得到离散l2模误差估计结果.最后给出具体的数值算例,以验证方法的实用性. 相似文献
15.
We propose a discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids. This numerical solver is a Lagrange–Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial masses. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are proven. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classic numerical tests. The results are compared with the approximate solutions obtained with the classic upwind Lagrange–Remap approach, and with experimental and previously published results of a reference test case. 相似文献
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We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the “fractional centered derivative” approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank–Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank–Nicolson method for the fractional diffusion equation with using fractional centered difference approach. 相似文献