Titlebook: An Introductory Guide to Computational Methods for the Solution of Physics Problems; With Emphasis on Spe George Rawitscher,Victo dos Santo

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黄油没有

Galerkin and Collocation Methods,ectral” methods, where the main emphasis is placed on establishing procedures to obtain the expansion coefficients. In this chapter, we present and compare two such methods: the Galerkin and the Collocation methods, with considerations about the nature of the support points employed by each.

小臼

Convergence of Spectral Approximations,ctral” methods that consist in expanding the solution to a particular problem in terms of a set of basis functions. We initially present theorems about the convergence of Fourier transforms, alongside with the accuracy of a Fourier spectral differentiation. Next, we present theorems concerning the c

Electrolysis

Chebyshev Polynomials as Basis Functions,pressions in terms of the powers of the variable ., where ., and the mesh points required for the Gauss–Chebyshev integration expression described in Chap. .. We also point out the advantage of the expansion into this set of functions, as their truncation error is spread uniformly across the . inter

充满装饰

The Integral Equation Corresponding to a Differential Equation,the advantages of working with the integral equation, called Lippmann–Schwinger (L–S). We show how a numerical solution of such an equation can be obtained by expanding the wave function in terms of Chebyshev polynomials, and give an example for a simple one-dimensional Schrödinger equation. This me

钝剑

Spectral Finite Element Method, polynomials called discrete variable representation (DVR). The coefficients of the expansion are obtained by a Galerkin method. When the radial domain is subdivided into contiguous partitions, the total procedure is called the spectral finite element method (FE-DVR). In each partition (or finite el

上釉彩

The Phase-Amplitude Representation of a Wave Function,ction is described in an efficient way by its amplitude .(.) and the wave phase .. Since each of these quantities vary monotonically and slowly with distance, they are much easier to calculate than the wave function itself. An iterative method to solve the non-linear equation for . is described, and

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