共查询到20条相似文献,搜索用时 9 毫秒
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We propose a new numerical method for modeling motion of open curves in two dimensions and open surfaces in three dimensions. Following the grid based particle method we proposed in [S. Leung, H.K. Zhao, A grid based particle method for moving interface problems. J. Comput. Phys. 228 (2009) 2993–3024], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The underlying grid is used to provide a quasi-uniform sampling and neighboring information for meshless particles. The key idea in the current paper is to represent and to track end-points of the open curve and boundary-points of the open surface explicitly and consistently with interior particles. We apply our algorithms to several applications including spiral crystal growth modeling and image segmentation using active contours. 相似文献
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In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method. 相似文献
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提出了一种基于二阶波动方程的(2M,4)高阶时域有限差分(FDTD)方法,通过使用辛积分传播子(SIP)在时域上获得4阶精度,使用离散奇异卷积(DSC)方法在空域上达到2M阶精度。与已有的(2M,4) 阶FDTD方法相比,虽然两者都采用SIP和DSC方法,但是此二者的不同点在于:第一,新方法基于二阶波动方程;第二,在离散计算空间时使用单一网格而不是传统的Yee网格;第三,单独计算某一场分量从而节约内存并减少计算量。数值计算结果表明,与传统高阶算法相比,基于波动方程的高阶FDTD方法耗费的机时只有它的50%,内存消耗下降10%, 而两者的计算结果之间相对误差小于5‰。 相似文献
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In this paper, a Birkhoff--Noether method of solving ordinary
differential equations is presented. The differential equations can
be expressed in terms of Birkhoff's equations. The first integrals
for differential equations can be found by using the Noether theory
for Birkhoffian systems. Two examples are given to illustrate the
application of the method. 相似文献
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The Hamilton--Jacobi method for solving ordinary differential equations is presented
in this paper. A system of ordinary differential equations of first order or second
order can be expressed as a Hamilton system under certain conditions. Then the
Hamilton--Jacobi method is used in the integration of the Hamilton system and the
solution of the original ordinary differential equations can be found. Finally, an
example is given to illustrate the application of the result. 相似文献
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The purpose of this paper is to provide a new method called the
Lagrange--Noether method for solving second-order differential
equations. The method is, firstly, to write the second-order
differential equations completely or partially in the form of
Lagrange equations, and secondly, to obtain the integrals of the
equations by using the Noether theory of the Lagrange system. An
example is given to illustrate the application of the result. 相似文献
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Methods of analytical mechanics for solving differential equations of first order 总被引:5,自引:0,他引:5
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A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton--Noether method, the
Lagrange--Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics. 相似文献
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We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for particles on the interface. It also renders neighborhood information among the meshless particles for local reconstruction of the interface. The resulting algorithm, which is based on Lagrangian tracking using meshless particles with Eulerian reference grid, can naturally handle/control topological changes. Moreover, adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad/oct-tree data structure. Extensive numerical examples are presented to demonstrate the capability of our new algorithm. 相似文献
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M. Grigoriu 《Journal of computational physics》2012,231(19):6495-6513
A method is proposed for solving equations with random entries, referred to as stochastic equations (SEs). The method is based on two recent developments. The first approximates the response surface giving the solution of a stochastic equation as a function of its random parameters by a finite set of hyperplanes tangent to it at expansion points selected by geometrical arguments. The second approximates the vector of random parameters in the definition of a stochastic equation by a simple random vector, referred to as stochastic reduced order model (SROM), and uses it to construct a SROM for the solution of this equation.The proposed method is a direct extension of these two methods. It uses SROMs to select expansion points, rather than selecting these points by geometrical considerations, and represents the solution by linear and/or higher order local approximations. The implementation and the performance of the method are illustrated by numerical examples involving random eigenvalue problems and stochastic algebraic/differential equations. The method is conceptually simple, non-intrusive, efficient relative to classical Monte Carlo simulation, accurate, and guaranteed to converge to the exact solution. 相似文献
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In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective. 相似文献
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M.A. Knyazev 《Reports on Mathematical Physics》1997,40(3):493-500
A direct method for solving constant coefficient nonlinear evolutional problems of mathematical physics extending the Hirota method to the case of degeneracy of k-parameter is described. An application of this method to the problem of finding the solutions describing coupled states in φ4-theory with damping is considered. 相似文献
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We sketch the integral variation method for generating approximate solutions to initial value problems involving systems of first-order ordinary differential equations. This new constructive technique is illustrated with applications to the damped oscillator, a nonlinear growth equation, and zonal harmonic perturbations of a near Earth satellite orbit. 相似文献
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George Adomian 《Foundations of Physics Letters》1993,6(6):603-605
In mathematical approaches to elementary particle theory, the equation [2 -
2/t2]=m2
;+g
3 has been of interest [1,2]; it describes a quartically self-coupled neutral scalar meson field. This paper applies the decomposition method [3-6] to obtain accurate non-perturbative timedevelopment of the field for this equation, or variations involving other nonlinear interactions, without the use of cutoff functions or truncations. 相似文献
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An improved algorithm is devised for using Fan sub-equation method to solve Wick-type stochastic partial differential equations. Applying the improved algorithm to the Wick-type generalized stochastic KdV equation, we obtain more general Jacobi and Weierstrass elliptic function solutions, hyperbolic and trigonometric function solutions, exponential function solutions and rational solutions. 相似文献
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A meshless scheme for partial differential equations based on multiquadric trigonometric B-spline quasi-interpolation
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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