Pseudo-spectral method stability
Pseudo-spectral methods, also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial differential equations. They are closely related to spectral methods, but complement the basis by … See more Take the initial-value problem $${\displaystyle i{\frac {\partial }{\partial t}}\psi (x,t)={\Bigl [}-{\frac {\partial ^{2}}{\partial x^{2}}}+V(x){\Bigr ]}\psi (x,t),\qquad \qquad \psi (t_{0})=\psi _{0}}$$ See more In a more abstract way, the pseudo-spectral method deals with the multiplication of two functions 1. See more The Fourier method If periodic boundary conditions with period $${\displaystyle [0,L]}$$ are imposed on the system, the basis functions can be generated by plane … See more
Pseudo-spectral method stability
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WebFeb 27, 2024 · This work presents a novel numerical stability analysis of a collection of pseudo-spectral methods, also known as split-step methods, for solving pulse … Webstability is regained with the 2/3-smoothing of pseudo-spectral Fourier method [42]; in the linear setup, the de-aliasing in the 2/3-method introduces sufficient smoothness …
WebMar 24, 2024 · [27] Gottlieb S., Wang C., Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D Viscous Burgers’ equation, J. Sci. Comput. 53 (2012) 102 – 128. Google Scholar [28] Greiner W., Relativistic Quantum Mechanics-Wave Equations, vol. 1, Springer, Berlin, Heidelberg, 1994. Google Scholar WebAbstract References Recommended Content Abstract In this paper we develop a stability theory for the Fourier (or pseudo-spectral) method for linear hyperbolic and parabolic partial differential equations with variable coefficients. Get full access to this article View all available purchase options and get full access to this article. Get Access
Web7-7 n inkx inkx 0 n dU ecinkUe dt += for n=1, …, N (16) where is a set of N ODE's for the coefficients U n. Finite difference is usually used for the time derivative. After U n is … WebMay 7, 2024 · A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the …
WebChebyshev pseudospectral collocation method for magneto-nanofluid flow through a porous channel with suction/injection at slowly expanding/contracting walls
WebPseudospectral methods Pseudospectral Methods ¾What is a pseudo-spectral Method? ¾Fourier Derivatives ¾The Acoustic Wave Equation with the Fourier Method … playstation 1 cheats and codesWebThe spectral Jacobi method (meth_cheb.4) satisfies the stability estimate (meth_cheb.13) with we proceed as follows. Squaring of (meth_cheb.7a) yields and we turn to estimate … primewire wolf wall streetWebfor the semidiscrete spectral and pseudo spectral approximation is of order s for com-patible initial data in the Sobolev space of order s + 1. In Section 5, conditions for stability … prime wire x fileshttp://twister.caps.ou.edu/CFD2024/Chapter7.pdf primewire yellowstoneWebNational Center for Biotechnology Information primewire you peopleWebNext, we apply the two pseudo-spectral methods to solve the nearly singular solution of the 3D incompress-ible Euler equations. We would like to see if the comparison we make regarding the convergence properties of the two pseudo-spectral methods for the 1D Burgers equation is still valid for the more challenging 3D incom-pressible Euler equations. playstation 1 console boxartWebFor the time integration high-order exponential operator splitting methods are studied, where the decomposition of the function defining the partial differential equation is chosen in accordance with the underlying spectral method. prime wire you knock on my door