scholarly journals Rapid convergence of the Weinberg expansion of the deuteron stripping amplitude

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
D. Y. Pang ◽  
N. K. Timofeyuk ◽  
R. C. Johnson ◽  
J. A. Tostevin
Keyword(s):  
Rapid Convergence ◽  
Deuteron Stripping

THE DETERMINATION OF DIGITAL WIENER FILTERS BY MEANS OF GRADIENT METHODS

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 310-326 ◽  
Author(s):  
R. J. Wang ◽  
S. Treitel
Keyword(s):  
Seismic Data ◽  
High Speed ◽  
Gradient Methods ◽  
Wiener Filter ◽  
Gradient Algorithm ◽  
Rapid Convergence ◽  
True Solution ◽  
Peripheral Device ◽  
Wiener Filters

The normal equations for the discrete Wiener filter are conventionally solved with Levinson’s algorithm. The resultant solutions are exact except for numerical roundoff. In many instances, approximate rather than exact solutions satisfy seismologists’ requirements. The so‐called “gradient” or “steepest descent” iteration techniques can be used to produce approximate filters at computing speeds significantly higher than those achievable with Levinson’s method. Moreover, gradient schemes are well suited for implementation on a digital computer provided with a floating‐point array processor (i.e., a high‐speed peripheral device designed to carry out a specific set of multiply‐and‐add operations). Levinson’s method (1947) cannot be programmed efficiently for such special‐purpose hardware, and this consideration renders the use of gradient schemes even more attractive. It is, of course, advisable to utilize a gradient algorithm which generally provides rapid convergence to the true solution. The “conjugate‐gradient” method of Hestenes (1956) is one of a family of algorithms having this property. Experimental calculations performed with real seismic data indicate that adequate filter approximations are obtainable at a fraction of the computer cost required for use of Levinson’s algorithm.

Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ming-Xian Lin ◽  
Chia-Hsiang Tseng ◽  
Chao Kuang Chen
Keyword(s):  
Decomposition Method ◽  
Large Deflection ◽  
Adomian Decomposition Method ◽  
Nonlinear Behavior ◽  
Bernoulli Beam ◽  
Rapid Convergence ◽  
Content Type ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam ◽  
Better Than

PurposeThis paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.Design/methodology/approachThe governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.FindingsThe results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.Originality/valueThe results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

Buckling of a viscous strut loaded eccentrically

1974 ◽  
Vol 9 (4) ◽  
pp. 227-229 ◽  
Author(s):  
J P Ellington
Keyword(s):  
Trigonometric Series ◽  
Series Solution ◽  
Maximum Deflection ◽  
Rapid Convergence ◽  
Poor Convergence

A solution to the problem of buckling of a viscous strut with eccentrically applied end loads has been found previously as an infinite trigonometric series having poor convergence for small values of time. An alternative series solution has been found, using powers rather than exponentials of time, which provides not only rapid convergence but simple closed forms for bounds on the maximum deflection.

Deuteron Stripping on Deformed Nuclei

1966 ◽  
Vol 151 (3) ◽  
pp. 853-874 ◽  
Author(s):  
P. J. Iano ◽  
N. Austern
Keyword(s):  
Deformed Nuclei ◽  
Deuteron Stripping

scholarly journals Rapid Convergence for Telegraph Systems with Periodic Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Peiguang Wang ◽  
Xiang Liu
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quasilinearization Method ◽  
Rapid Convergence ◽  
Forcing Function

The generalized quasilinearization method is applied in this paper to a telegraph system with periodic boundary conditions. We consider the case in which the forcing function F(t,x,U) satisfies the following condition: ∂n-1F(t,x,U)/∂Un-1 exists and is quasimonotone nondecreasing or nonincreasing. We develop nonlinear iterates of order n-1 which will be different with n being even or odd. Finally, we develop two sequences which converge to the solution of the telegraph system and the convergence is of order n.

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