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Coupled with the Houbolt method, a third order finite difference time marching scheme, the method of approximate particular solutions (MAPS) has been applied to solve wave equations. Radial basis function has played an important role in the solution process of the MAPS. To show the effectiveness of the MAPS, we compare the results with the well known Kansa's method, timemarching method of fundamental solutions (TMMFS), and traditional finite element methods. To validate the effectiveness and easiness of the MAPS, four numerical examples which including regular, smooth irregular, and non-smooth domains are given. 相似文献
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本文考虑广义Camassa-Holm方程。采用微分方程定性分析、动力系统分支、相平面分析、精确计算、微分方程数值模拟等相结合的办法,对该方程的有界行波进行比较系统研究,得到关于定常态的奇点类型和分支解等。用计算机绘出了所得函数的图形,同时也从方程本身出发,模拟出了有界波的平面图,理论结果和数值模拟互相验证了其正确性。 相似文献
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This paper describes the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations by utilizing the direct determinant search method. The complex-valued kernels are used in the MFS in order to avoid the spurious eigenvalues. The benchmark problems of a circular plate with clamped, simply supported and free boundary conditions are studied analytically as well as numerically using the discrete and continuous versions of the MFS schemes to demonstrate the major results of the present paper. Namely only true eigenvalues are contained and no spurious eigenvalues are included in the range of direct determinant search method. Consequently analytical derivation is carried out by using the degenerate kernels and Fourier series to obtain the exact eigenvalues which are used to validate the numerical methods. The MFS is free from meshes, singularities, and numerical integrations. As a result, the proposed numerical method can be easily used to solve plate vibrations free from spurious eigenvalues in simply connected domains. 相似文献
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S. Chantasiriwan 《International journal for numerical methods in engineering》2006,66(1):147-165
A time‐dependent heat conduction problem can be solved by the method of fundamental solutions using the fundamental solution to the modified Helmholtz equation or the fundamental solution to the heat equation. This paper presents solutions using both formulations in terms of initial and boundary conditions. Such formulations enable calculation of errors and variance, which indicates sensitivities of solutions to uncertainties in initial and boundary conditions. Both errors and variance of solutions to three test problems by the two methods of fundamental solutions are used to compare performances of the methods. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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In this work we show the application of the Method of Fundamental Solutions(MFS) in the determination of eigenfrequencies and eigenmodes associated to wave scattering problems. This meshless method was already applied to simple geometry domains with Dirichlet boundary conditions (cf. Karageorghis (2001)) and to multiply connected domains (cf. Chen, Chang, Chen, and Chen (2005)). Here we show that a particular choice of point-sourcescan lead to very good results for a fairly general type of domains. Simulations with Neumann boundary conditionare also considered. 相似文献
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欧拉方程是流体力学中非常重要的模型,被广泛应用于许多领域.构造它的精确解是数学物理中非常有意义的工作.精确解可以为理解它的非线性现象和物理意义提供具体的例子.本文旨在通过不变子空间方法构造可压缩欧拉方程的精确解.在变量变换意义下,由不变条件给出与可压缩方程相关的不变子空间;在这些不变子空间中,它被约化为一阶常微分方程组;通过求解这些常微分方程组,最终得到可压缩欧拉方程的一些精确解. 相似文献
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The method of fundamental solutions is a meshless method. Only boundary collocation points are needed during the whole solution process. It has the merits of mathematical simplicity, ease of programming, high solution accuracy, and others. In this paper, the method of fundamental solutions is applied to simulate 2D steady-state groundwater flow problems. The principle of superposition is used during the whole solution process. Numerical results are compared with the multiquadrics method and the mixed finite element method as well as analytical solutions. It is shown that the method of fundamental solutions is promising in dealing with steady groundwater flow problems. 相似文献
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通过行波约化一类(3+1)维非线性波动方程和建立与立方非线性Klejn-Gordon方程间变换的联系,由此得到其孤立波解和周期解。 相似文献
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The telegraph equations are solved by using the meshless numerical method called the time-marching method of fundamental solutions (TMMFS) in this paper. The present method is based on the method of fundamental solutions, the method of particular solutions and the Houbolt finite difference scheme. The TMMFS is a meshless numerical method, and has the advantages of no mesh building and numerical quadrature. Therefore in this study we eventually solved the multi-dimensional telegraph equation problems in irregular domain. There are totally six numerical examples demonstrated, in order they are one-dimensional telegraph equation, one-dimensional non-decaying telegraph problem, two-dimensional telegraph equation in irregular domain, three-dimensional telegraph problem in cubic domain, three-dimensional telegraph equation in irregular domain and three-dimensional fixed boundary telegraph problem in irregular domain. All numerical results have shown good efficiency and accuracy of the algorithm, thus demonstrated the present meshless numerical method of the TMMFS is applicable for further applications in solving the multi-dimensional telegraph equation in irregular domain. 相似文献
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用动力系统的定性分析理论和分支方法,对带有色散项的Degasperis-Proces方程的周期尖波解和单孤子解进行了研究.给出了Degasperis-Procesi方程对应行波系统的相图分支,利用相图从两种不同方式构造了孤立尖波解的解析表达式,并通过数值模拟给出了部分解的图像. 相似文献
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In this article, a meshless numerical method for solving the inverse source problem of the space-fractional diffusion equation is proposed. The numerical solution is approximated using the fundamental solution of the space-fractional diffusion equation as a basis function. Since the resulting matrix equation is extremely ill-conditioned, a regularized solution is obtained by adopting the Tikhonov regularization scheme, in which the choice of the regularization parameter is based on generalized cross-validation criterion. Two typical numerical examples are given to verify the efficiency and accuracy of the proposed method. 相似文献
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本文利用变分法和Hardy不等式讨论了一类带奇异系数临界半线性椭圆方程,在一定条件下证明了方程解的存在性,并得到了解的存在性的两个充分条件。 相似文献
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本文研究了一类高阶非线性中立型差分方程组多正解的存在性。通过构造实Banach空间中的严格集压缩算子及利用不动点指数理论,得到了这类方程组两个正解的存在性准则。所得结论推广并改进了已有的相关结果。 相似文献
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C. S. Chen M. A. Golberg Y. C. Hon 《International journal for numerical methods in engineering》1998,43(8):1421-1435
The Laplace transform is applied to remove the time-dependent variable in the diffusion equation. For non-harmonic initial conditions this gives rise to a non-homogeneous modified Helmholtz equation which we solve by the method of fundamental solutions. To do this a particular solution must be obtained which we find through a method suggested by Atkinson. To avoid costly Gaussian quadratures, we approximate the particular solution using quasi-Monte-Carlo integration which has the advantage of ignoring the singularity in the integrand. The approximate transformed solution is then inverted numerically using Stehfest's algorithm. Two numerical examples are given to illustrate the simplicity and effectiveness of our approach to solving diffusion equations in 2-D and 3-D. © 1998 John Wiley & Sons, Ltd. 相似文献