- Referenced in 127 articles
- interface between two grid cells into waves propagating into the neighboring cells. Adaptive mesh refinement ... working on extensions to parabolic equations as well. The “wave propagation” algorithms implemented in Clawpack...
- Referenced in 88 articles
- finding travelling solitary wave solutions to nonlinear evolution equations. A Maple package RATH which outputs ... polynomial travelling solitary wave solutions of a given nonlinear evolution equation is presented. The effectiveness...
- Referenced in 29 articles
- package for solving 2D visco-acoustic wave equation. Frequency-domain finite-difference (FDFD) modelling ... presented which solves 2D visco-acoustic wave equation. The mixed-grid stencil is used...
- Referenced in 362 articles
- used in realistic applications with primitive equation models for the ocean and atmosphere. A recent ... Dana McKenzie suggests that the killer heat wave that hit Central Europe in the summer...
- Referenced in 35 articles
- find exact traveling wave solutions of differential-difference equations in terms of tanh functions ... tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package ... automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package...
- Referenced in 64 articles
- Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems. The authors present a generalisation ... Euler equations of gas dynamics to employ high-resolution wave-propagation algorithms in a more ... variety of new problems, including hyperbolic equations, which are not in a conservation form, problems...
- Referenced in 16 articles
- self-adjoint scalar wave equation on a Petrov type D spacetime. A decomposition ... spinor of a non-self-adjoint scalar wave operator is algebraically degenerate and its principal...
Differentiation Matrix Suite
- Referenced in 225 articles
- MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented ... fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability...
- Referenced in 14 articles
- that are solutions to an approximate wave equation with a weighted potential. The weighting factors...
- Referenced in 12 articles
- solution of the one-dimensional wave equation...
- Referenced in 152 articles
- authors for solving shallow water equations in spherical geometry are applied to seven test cases ... over an isolated mountain, (vi) Rossby-Haurwitz wave, and (vii) observed atmospheric states...
- Referenced in 11 articles
- solution of the Schrödinger and Dirac wave equations for central fields. Nature of problem: This ... numerical solutions of the Schrodinger and Dirac equations for central fields such that ... finite for r=0. Radial wave functions, eigenvalues for bound states and phase shifts...
- Referenced in 53 articles
- Baer-Nunziato equations of compressible two-phase flow for the “subsonic” wave configuration. The solver ... Riemann problem. In particular, stationary contact waves are resolved exactly. We then implement and test ... HLLC solver for the Baer-Nunziato equations in the framework of finite volume, discontinuous Galerkin...
- Referenced in 9 articles
- obtaining conditional symmetries of the nonlinear wave equation u t =(uu x ) x invariant...
- Referenced in 8 articles
- Laplace, Helmholtz, Lame, and wave equations...
- Referenced in 5 articles
- discontinuous Galerkin discretization of the elastic wave equation in second order form. We present ... spatial discretizations of the linear elastic wave equation. The resulting methods are stable and, depending...
- Referenced in 22 articles
- wave approximate Riemann solver is used. The induction equation is treated by adopting the Upwind ... propagation of large amplitude circularly polarized Alfven waves. In particular, we show that reconstruction based...
- Referenced in 20 articles
- investigating periodic travelling wave solutions of partial differential equations. Typically such equations will contain ... control parameter. Focussing on periodic travelling waves introduces an additional parameter, the wave speed...
- Referenced in 14 articles
- series of exact traveling wave solutions for nonlinear evolution equations. In Maple 8, by taking ... elliptic equation method. RAEEM can entirely automatically output a series of exact traveling wave solutions ... applying it to a large variety of equations. In addition to recovering previously known solutions...
- Referenced in 6 articles
- multiple sources for the scalar Helmholtz equation We propose an algorithm to compute an approximate ... frequency time-harmonic wave equation with broadband and multi-point illumination. This model finds many...