標(biāo)題: Titlebook: An Introductory Guide to Computational Methods for the Solution of Physics Problems; With Emphasis on Spe George Rawitscher,Victo dos Santo [打印本頁(yè)] 作者: MASS 時(shí)間: 2025-3-21 18:49
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書目名稱An Introductory Guide to Computational Methods for the Solution of Physics Problems讀者反饋
書目名稱An Introductory Guide to Computational Methods for the Solution of Physics Problems讀者反饋學(xué)科排名
作者: 黃油沒(méi)有 時(shí)間: 2025-3-22 00:00
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.作者: 小臼 時(shí)間: 2025-3-22 04:00
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作者: Electrolysis 時(shí)間: 2025-3-22 07:45
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作者: 充滿裝飾 時(shí)間: 2025-3-22 10:41
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 Schr?dinger equation. This me作者: 鈍劍 時(shí)間: 2025-3-22 15:01
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作者: 上釉彩 時(shí)間: 2025-3-22 17:13
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作者: 詞匯 時(shí)間: 2025-3-22 21:35 作者: POINT 時(shí)間: 2025-3-23 01:24 作者: guzzle 時(shí)間: 2025-3-23 06:49 作者: 后天習(xí)得 時(shí)間: 2025-3-23 10:55
https://doi.org/10.1007/978-3-322-98672-6er-Cromer method. The emphasis here is on algorithm errors, and an explanation of what is meant by the “order” of the error. We show that the Euler method introduces an error of order 2, denoted as . while the latter presents errors of order .. We finish the chapter by applying the methods to two im作者: 減震 時(shí)間: 2025-3-23 15:36 作者: 慎重 時(shí)間: 2025-3-23 21:49 作者: glomeruli 時(shí)間: 2025-3-23 23:53
https://doi.org/10.1007/978-3-642-71903-5pressions 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作者: 除草劑 時(shí)間: 2025-3-24 05:15
https://doi.org/10.1007/978-3-662-41281-7the 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 Schr?dinger equation. This me作者: gorgeous 時(shí)間: 2025-3-24 07:08 作者: Flatter 時(shí)間: 2025-3-24 12:43
Die Bestimmung der Umtriebszeitction 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作者: Intercept 時(shí)間: 2025-3-24 15:47 作者: 口味 時(shí)間: 2025-3-24 19:22 作者: sed-rate 時(shí)間: 2025-3-25 01:15 作者: 魔鬼在游行 時(shí)間: 2025-3-25 06:39
George Rawitscher,Victo dos Santos Filho,Thiago CaEmphasizes some advantages of spectral methods.Includes a comparison with finite element and finite difference methods.Includes programs in MATLAB to implement the algorithms作者: 斜谷 時(shí)間: 2025-3-25 09:40
http://image.papertrans.cn/a/image/155614.jpg作者: meritorious 時(shí)間: 2025-3-25 13:08
Die Bestimmung der UmtriebszeitIn this chapter we show that spectral methods can be applied to a third-order differential equation. Such an equation can be solved by a Collocation method with Chebyshev polynomials and without the application of Green’s functions.作者: 總 時(shí)間: 2025-3-25 17:10 作者: 使糾纏 時(shí)間: 2025-3-25 22:10 作者: deactivate 時(shí)間: 2025-3-26 02:28
Conclusions,We discuss here the main topics developed in this monograph. Through our analysis, examples and calculations, we show that spectral methods present various advantages in relation to the methods based on finite differences in terms of accuracy, convergence, time of computation and stability.作者: antidepressant 時(shí)間: 2025-3-26 06:45 作者: 遺產(chǎn) 時(shí)間: 2025-3-26 08:47
https://doi.org/10.1007/978-3-319-42703-4Spectral Computational Methods; Finite-difference methods; Fourier spectral Differentiation Matrices; Q作者: 上流社會(huì) 時(shí)間: 2025-3-26 12:42
978-3-319-42702-7Springer Nature Switzerland AG 2018作者: 分發(fā) 時(shí)間: 2025-3-26 16:56 作者: 得罪人 時(shí)間: 2025-3-26 22:11
Book 2018acks.?.During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and?.the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points?.used in finite difference methods. In particular, they dem作者: 細(xì)查 時(shí)間: 2025-3-27 04:47
ons and?.the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points?.used in finite difference methods. In particular, they dem978-3-319-42702-7978-3-319-42703-4作者: institute 時(shí)間: 2025-3-27 08:10 作者: thyroid-hormone 時(shí)間: 2025-3-27 10:16
An Introductory Guide to Computational Methods for the Solution of Physics Problems978-3-319-42703-4作者: flourish 時(shí)間: 2025-3-27 15:01
MATLAB to implement the algorithmsThis monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally?.taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to?.the solution of physica作者: Brain-Waves 時(shí)間: 2025-3-27 21:21 作者: 過(guò)于光澤 時(shí)間: 2025-3-27 22:02
https://doi.org/10.1007/978-3-642-91935-0the Galerkin–Fourier expansion method and the spectral Green’s function collocation method. The vibration frequencies are obtained as the eigenvalues of the corresponding matrices. We compare the advantages and disadvantages of both methods.作者: Capture 時(shí)間: 2025-3-28 03:43 作者: 無(wú)法破譯 時(shí)間: 2025-3-28 09:21
Finite Difference Methods,thod introduces an error of order 2, denoted as . while the latter presents errors of order .. We finish the chapter by applying the methods to two important physical problems: the physics of the pendulum and the physics of descending parachutes.作者: 側(cè)面左右 時(shí)間: 2025-3-28 12:03
The Vibrating String,the Galerkin–Fourier expansion method and the spectral Green’s function collocation method. The vibration frequencies are obtained as the eigenvalues of the corresponding matrices. We compare the advantages and disadvantages of both methods.作者: 馬具 時(shí)間: 2025-3-28 17:29
Iteratively Calculated Eigenvalues,btain the wave functions required in the procedure can improve the precision to . The numerical application that we present here is again based on the vibration frequencies of an inhomogeneous string as presented in Chap.?.. To close the chapter, we propose a project which applies the method to the case of an exponential attractive potential.作者: Overstate 時(shí)間: 2025-3-28 20:42
Convergence of Spectral Approximations,alculation of the interpolation error and the determination of the set of functions that gives rise to the best interpolation in such methods. In last section, we present assignments in order to analyze the rate of convergence and the error of various sets of basis functions in an expansion.作者: vertebrate 時(shí)間: 2025-3-29 00:16
Chebyshev Polynomials as Basis Functions,val with the smallest error for functions that do not have strong singularities. The convergence of the expansion of functions in terms of Chebyshev polynomials will be illustrated, as well as the accuracy of the calculation of integrals and of derivatives. A novel “hybrid” method for calculating derivatives of higher order will also be described.作者: Eeg332 時(shí)間: 2025-3-29 03:52 作者: 表臉 時(shí)間: 2025-3-29 08:27
https://doi.org/10.1007/978-3-642-91935-0We also show how these functions serve to obtain a separable representation of a general operator (for example of a non-local potential), and we describe the iterative corrections of the truncation error in a Sturmian expansion.作者: insert 時(shí)間: 2025-3-29 14:12
Sturmian Functions,We also show how these functions serve to obtain a separable representation of a general operator (for example of a non-local potential), and we describe the iterative corrections of the truncation error in a Sturmian expansion.作者: A保存的 時(shí)間: 2025-3-29 15:59 作者: coalition 時(shí)間: 2025-3-29 22:03 作者: Apraxia 時(shí)間: 2025-3-30 01:51 作者: 修飾 時(shí)間: 2025-3-30 05:05
https://doi.org/10.1007/978-3-662-41281-7gorithm is of the Galerkin type. We compare the errors and the speed of calculation of the FE-DVR with those of the S-IEM, where the basis functions are Chebyshev polynomials, and the algorithm is of the Collocation type.作者: 氣候 時(shí)間: 2025-3-30 08:29
Die Bestimmung der Umtriebszeit case the wave function is oscillatory); and (b) when the potential is larger than the incident energy (this is the case of the classically forbidden region). Various applications and their accuracies are also described in this chapter.
