Related papers: Wave solutions of Gilson-Pickering equation
Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the gravitational potential for each…
In this paper we apply the newly born choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Some people complain that Luh's choice theory, based on harmonic analysis, is…
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…
This paper contains a brief sketch of some methods that can be used to obtain the Wigner function for a number of systems. We give an overview of the technique as it is applied to some simple differential systems related to diffusion…
When solving the Poisson equation by the finite element method, we use one degree of freedom for interpolation by the given Laplacian - the right hand side function in the partial differential equation. The finite element solution is the…
We study an approximation method for the one-dimensional nonlinear filtering problem, with discrete time and continuous time observation. We first present the method applied to the Fokker-Planck equation. The convergence of the…
We introduce a generalization of Glimm's random choice method, which provides us with an approximation of entropy solutions to quasilinear hyperbolic system of balance laws. The flux-function and the source term of the equations may depend…
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…
In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of…
We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main…
In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (on each element) are constructed by the geometric optics…
In this paper, a new exact solution of general Degasperis-Procesi (gDP) equation, a nonlinear equation in plasma, will be constructed by using PPA method, extended trigonometry and extended hyperbolic method. gDP equation is a good…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG) for hyperbolic equations with random and singular coefficients. Due to the singu- lar nature of the solution, the standard gPC-SG methods may suffer from a poor or…
The fundamental solution for the wave equation in n variables is built from the simple one-dimensional formula, via an integral representation of the cosine of the sum of squares of self-adjoint operators. Representation formulas are given…
This report summarizes progress made towards a new approach for enlarging the dynamic aperture of particle accelerators. Unlike prior methods which attempted to move the location of select resonances outward in phase space, our approach…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the timestep size ($h$-method), we achieve accuracy by increasing the order of the method…
This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…
A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is…