WebWe consider spectral and pseudo-spectral Jacobi-Galerkin methods and corresponding iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. The Gauss-Jacobi quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak ... 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 $${\displaystyle V(x)}$$ and 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
(PDF) Comparison of Lattice and Pseudo 3D Numerical
WebJul 1, 2024 · The Fourier pseudo-spectral method is used for problems in which there is a natural periodicity. In multi-dimensional problems it should be used only in those … WebJun 17, 2016 · A brief introduction to pseudo-spectral methods: application to diffusion problems. Denys Dutykh. The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type ... note for loss of grandmother
The Pseudo-spectral method and Matlab Implement - Springer
Web7.2. Pseudo-spectral method. Such aliasing errors also appear when evaluating a convolution sum via Fourier transforms. To understand this, compare the nonlinear term in equations (6.2) and (7.3): The difference is the appearance of the term … + n ⋅ N in the expression computed via the FFT. For the computed result to be correct, measures ... WebNext, 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. WebOct 28, 1998 · A Practical Guide to Pseudospectral Methods. During the past two decades, pseudospectral methods have emerged as successful, and often superior, alternatives to … how to set environment variables linux