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1.
A. G. Bratsos 《Numerical Algorithms》2006,43(4):295-308
A three-time level finite-difference scheme based on a fourth order in time and second order in space approximation has been
proposed for the numerical solution of the nonlinear two-dimensional sine-Gordon equation. The method, which is analysed for
local truncation error and stability, leads to the solution of a nonlinear system. To avoid solving it, a predictor–corrector
scheme using as predictor a second-order explicit scheme is proposed. The procedure of the corrector has been modified by
considering as known the already evaluated corrected values instead of the predictor ones. This modified scheme has been tested
on the line and circular ring soliton and the numerical experiments have proved that there is an improvement in the accuracy
over the standard predictor–corrector implementation.
This research was co-funded by E.U. (75%) and by the Greek Government (25%). 相似文献
2.
Athanassios G. Bratsos 《Numerical Algorithms》2007,46(1):45-58
A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants
to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme,
which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector
are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values
are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already
known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq
equation and conclusions from the relevant known results are derived.
相似文献
3.
The problem of computing light scattering by cylindrical fibers with high aspect ratio in the framework of the Null‐Field method with discrete sources is treated. Numerical experiments for investigating the scattering properties of two fiber geometries are performed using distributed spherical vector wave functions as discrete sources. 相似文献
4.
Hyungjin Huh 《Journal of Functional Analysis》2007,242(2):526-549
We study low regularity solutions of the Chern-Simons-Higgs equations. The Lorentz gauge condition makes them hyperbolic equations with the null form. Under the Coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation. The div-curl decomposition is used in the temporal gauge. 相似文献
5.
Our new trigonometrically fitted predictor–corrector (P–C) schemes presented here are based on the well known Adams–Bashforth–Moulton methods: the predictor is based on the fifth order Adams–Bashforth scheme and the corrector on the sixth order Adams–Moulton scheme. We tested the efficiency of our newly developed schemes against well known methods, with excellent results. The numerical experiments showed that at least one of our schemes is noticeably more efficient compared to other methods, some of which are specially designed for this type of problem. It is also worth mentioning that this is the first time that sixth algebraic order trigonometrically fitted Adams–Bashforth–Moulton P–C schemes are used to efficiently solve the radial Schrödinger equation.Active Member of the European Academy of Sciences and Arts 相似文献
6.
A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
7.
An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ2n+2) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
9.
With the exponential growth of genome databases, the importance of phylogenetics has increased dramatically over the past years. Studying phylogenetic trees enables us not only to understand how genes, genomes, and species evolve, but also helps us predict how they might change in future. One of the crucial aspects of phylogenetics is the comparison of two or more phylogenetic trees. There are different metrics for computing the dissimilarity between a pair of trees. The Robinson-Foulds (RF) distance is one of the widely used metrics on the space of labeled trees. The distribution of the RF distance from a given tree has been studied before, but the fastest known algorithm for computing this distribution is a slow, albeit polynomial-time, O(l5) algorithm. In this paper, we modify the dynamic programming algorithm for computing the distribution of this distance for a given tree by leveraging the number-theoretic transform (NTT), and improve the running time from O(l5) to O(l3 log l), where l is the number of tips of the tree. In addition to its practical usefulness, our method represents a theoretical novelty, as it is, to our knowledge, one of the rare applications of the number-theoretic transform for solving a computational biology problem. 相似文献
10.