We solve the Cauchy problem for the n-dimensional wave equation using elementary properties of the Fourier transform.Additional informationAuthor informationAlberto TorchinskyALBERTO TORCHINSKY received his Licenciado en Matemáticas from the Universidad Nacional de Buenos Aires in 1966, and his Ph.D. from...
Fast Fourier transformLeap-Frog methodSolitary wavesThe modified regularized long wave (MRLW) equation is numerically solved using Fourier spectral collection method. The MRLW equation is discretized in space variable by the Fourier spectral method and Leap-Frog method for time dependence. To validate...
The one-dimensional wave equation is given by (1) In order to specify a wave, the equation is subject to boundary conditions (2) (3) and initial conditions (4) (5) The one-dimensional wave equation can be solved exactly by d'Alembert's solution, using a Fourier transform ...
An incremental-iterative solution based on the Newmark direct integration method and the Newton鈥揜aphson method is adopted for solving the nonlinear equation... HT Thai,SE Kim - 《Finite Elements in Analysis & Design》 被引量: 138发表: 2011年 Comparison and verification of numerical reconstructio...
摘要: The relationship between the Poincaré and Galilei groups allows us to write the Poincaré wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied....
Tappert, "Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations," SIAM Review, vol. Parabolic Equation Modeling of Propagation over Terrain Using Digital Elevation Model In the simulation of ocean tidal waves, Eulerian schemes are...
The Fourier Transform is typically calculated using an integral equation that involves the original function and the frequency variable. There are also various numerical methods and algorithms that can be used to compute the Fourier Transform.
[1] A standard method for modeling electromagnetic propagation in the troposphere is the Fourier split-step algorithm for solving the parabolic wave equation. An important advance in this technique was the introduction of the mixed Fourier transform, which permitted the extension of the method from ...
waves: scaling ascertains the relative importance of the different components of the flow, and in this geophysical regime the (linear) contribution due to the Earth’s rotation to the longitudinal momentum equation balances the linear part of the material derivative, both being of the same order....
(2.76) using integral transform techniques. To begin, a new field variable, W = W(R;ω), is introduced, defined by (2.77)G=WR. When this expression is substituted into Eq. (2.76), the Helmholtz equation becomes (2.78)1R∂∂R(R∂W∂R)−W4R2+k2W=S32πδ(R)R3/2. ...