scholarly journals A numerical solution of problems in calculus of variation using direct method and nonclassical parameterization

2010 ◽  
Vol 234 (5) ◽  
pp. 1364-1373 ◽  
Author(s):  
Mohammad Maleki ◽  
Mahmoud Mashali-Firouzi
Keyword(s):  
Numerical Solution ◽  
Direct Method ◽  
Calculus Of Variation

A direct method for the numerical solution ofy″=f(x,y)

CALCOLO ◽  
1984 ◽  
Vol 21 (4) ◽  
pp. 369-377 ◽  
Author(s):  
S. H. Chang ◽  
P. C. Gnepp
Keyword(s):  
Numerical Solution ◽  
Direct Method ◽  
A Direct Method

scholarly journals THE NUMERICAL SOLUTION BY THE METHOD OF DIRECT INTEGRALS OF DIFFERENTIATION OF EQUATIONS HAVE AN APPLICATION IN THE GAS FILTRATION THEOREM

2020 ◽  
pp. 147-153
Author(s):  
Abdujabbor Abdurazakov ◽  
Nasiba Makhmudova ◽  
Nilufar Mirzamakhmudova
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Error Estimate ◽  
Numerical Solution ◽  
Direct Method ◽  
Gas Filtration ◽  
Sweep Method ◽  
Time Step

On the basis of the direct method and a combination of differential sweep, the article developed a calculated algorithm for solving gas filtration, thereby taking into account the convergence of the approximate solution to the exact one. KEYWORDS: direct method, sweep method, differential equation, time step, convergence, approximate solution, error estimate.

scholarly journals The Numerical Solution of Problems in Calculus of Variation Using B-Spline Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. Zarebnia ◽  
M. Birjandi
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Subsequent Development ◽  
Algebraic Equations ◽  
Spline Collocation ◽  
Calculus Of Variation ◽  
B Spline ◽  
Spline Collocation Method

A B-spline collocation method is developed for solving boundary value problems which arise from the problems of calculus of variations. Some properties of the B-spline procedure required for subsequent development are given, and they are utilized to reduce the solution computation of boundary value problems to some algebraic equations. The method is applied to a few test examples to illustrate the accuracy and the implementation of the method.

scholarly journals Solutions of the (free boundary) Reifenberg Plateau problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Camille Labourie
Keyword(s):  
Free Boundary ◽  
Weak Convergence ◽  
Direct Method ◽  
Weak Limit ◽  
Plateau Problem ◽  
Minimizing Sequence ◽  
Calculus Of Variation ◽  
Link Type ◽  
Weak Limits

AbstractWe solve two variants of the Reifenberg problem for all coefficient groups. We carry out the direct method of the calculus of variation and search a solution as a weak limit of a minimizing sequence. This strategy has been introduced by De Lellis, De Philippis, De Rosa, Ghiraldin and Maggi and allowed them to solve the Reifenberg problem. We use an analogous strategy proved in [C. Labourie, Weak limits of quasiminimizing sequences, preprint 2020, https://arxiv.org/abs/2002.08876] which allows to take into account the free boundary. Moreover, we show that the Reifenberg class is closed under weak convergence without restriction on the coefficient group.

Characterization of frozen hydrated biological specimens by low-loss EELS

1992 ◽  
Vol 50 (2) ◽  
pp. 1572-1573
Author(s):  
Songquan Sun ◽  
Richard D. Leapman
Keyword(s):  
Water Content ◽  
Direct Method ◽  
Internal Standard ◽  
Dry Weight ◽  
Dark Field ◽  
Protein Solutions ◽  
Subcellular Compartment ◽  
Differential Shrinkage ◽  
Electron Energy Loss

Analyses of ultrathin cryosections are generally performed after freeze-drying because the presence of water renders the specimens highly susceptible to radiation damage. The water content of a subcellular compartment is an important quantity that must be known, for example, to convert the dry weight concentrations of ions to the physiologically more relevant molar concentrations. Water content can be determined indirectly from dark-field mass measurements provided that there is no differential shrinkage between compartments and that there exists a suitable internal standard. The potential advantage of a more direct method for measuring water has led us to explore the use of electron energy loss spectroscopy (EELS) for characterizing biological specimens in their frozen hydrated state.We have obtained preliminary EELS measurements from pure amorphous ice and from cryosectioned frozen protein solutions. The specimens were cryotransfered into a VG-HB501 field-emission STEM equipped with a 666 Gatan parallel-detection spectrometer and analyzed at approximately −160 C.

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