Topic
Numerical analysis
About: Numerical analysis is a research topic. Over the lifetime, 52236 publications have been published within this topic receiving 1224230 citations. The topic is also known as: numerical computation & numerical mathematics.
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Book•
01 Jan 1966
TL;DR: Reference Record created on 2005-11-18, modified on 2016-08-08 as discussed by the authors, created on 2011-11 -18, created on 2006-11 18 and modified on 2008-08 -08,08
Abstract: Keywords: analyse ; methodes : numeriques ; equations : lineaires ; calcul : integral ; equations : differentielles Reference Record created on 2005-11-18, modified on 2016-08-08
2,377 citations
TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Abstract: In this paper, a new kind of analytical technique for a non-linear problem called the variational iteration method is described and used to give approximate solutions for some well-known non-linear problems. In this method, the problems are initially approximated with possible unknowns. Then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Being different from the other non-linear analytical methods, such as perturbation methods, this method does not depend on small parameters, such that it can find wide application in non-linear problems without linearization or small perturbations. Comparison with Adomian’s decomposition method reveals that the approximate solutions obtained by the proposed method converge to its exact solution faster than those of Adomian’s method.
2,371 citations
TL;DR: A new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation, which can easily handle topology changes and is strongly dependent on the initial guess.
2,176 citations
TL;DR: In this paper, a numerical method for the dynamic analysis of infinite continuous systems is developed, applicable to systems for which all exciting forces and geometrical irregularities are confined to a limited region and is applicable to both transient and steady state problems.
Abstract: A numerical method for the dynamic analysis of infinite continuous systems is developed. The method is applicable to systems for which all exciting forces and geometrical irregularities are confined to a limited region and is applicable to both transient and steady state problems. The infinite system is replaced by a system consisting of a finite region subjected to a boundary condition which simulates an energy absorbing boundary. The resulting systems may be analyzed by the finite element method. Examples applying the method to foundation vibration problems are presented. Good agreement with existing solutions is found and new results for embedded footings are presented.
2,172 citations
Book•
01 Jan 1976
TL;DR: Numerical methods in finite element analysis, Numerical techniques in finite elements analysis, and so on.
Abstract: Numerical methods in finite element analysis , Numerical methods in finite element analysis , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
2,085 citations