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Variational Methods for Evolution
Oberwolfach Reports, 2012The meeting focused on the last advances in the applications of variational methods to evolution problems governed by partial differential equations. The talks covered a broad range of topics, including large deviation and variational principles, rate-independent evolutions and gradient flows, heat flows in metric-measure spaces, propagation of ...
Alexander Mielke +3 more
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2004
In many cases stationary perturbation theory cannot be applied successfully as there may not be a closely related problem which is capable of exact solution.
S. Lokanathan, Ajoy Ghatak
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In many cases stationary perturbation theory cannot be applied successfully as there may not be a closely related problem which is capable of exact solution.
S. Lokanathan, Ajoy Ghatak
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On the Palatini method of variation
Journal of Mathematical Physics, 1978The Palatini method of variation is compared with the Hilbert method for symmetric metrics and affine connections. It is found that the two methods are in general inequivalent. The Hilbert method is recommended as being more general.
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Variational Methods of Approximation [PDF]
, 1976 In this chapter, we describe several of the more popular variational methods for the approximate solution of boundary-and initial-value problems. For ease in presentation, we confine our attention to linear problems, and most of what we present has to do with elliptic boundary-value problems. In particular, we discuss interpolation properties of finite
J. N. Reddy, J. T. Oden
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The Schwinger Variation Method
Journal of the Society for Industrial and Applied Mathematics, 1964Abstract : The Schwinger variation method is removed from its customary setting in Green's function theory, and is approached from the integral equations viewpoint. The traditional Schwinger theory is improved upon in two respects. Error bounds are provided for the approximations to A(f), a function determining waveguide transmission and reflection ...
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Variational transcorrelated method
The Journal of Chemical Physics, 2010We propose a new approach to the use of Jastrow ansatz in the calculation of electron correlations, based on a modification of the transcorrelated method of Boys and Handy [Proc. R. Soc. London, Ser. A 309, 209 (1969)]. In this new method, the original transcorrelated orbital equation is replaced with a general variational equation for the reference ...
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The variational collocation method
Computer Methods in Applied Mechanics and Engineering, 2016We propose the variational collocation method for the numerical solution of partial differential equations. The conceptual basis is the establishment of a direct connection between the Galerkin method and the classical collocation methods, with the perspective of achieving the accuracy of the former with a computational cost of one point evaluation per
Hector Gomez, Laura De Lorenzis
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2000
Our final perturbation technique is the variational technique, which is particularly well-suited for finding approximations to ground-state energies and wave functions. We shall apply it, in particular, to find approximations to the ground-state energy and wave functions for the He atom.
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Our final perturbation technique is the variational technique, which is particularly well-suited for finding approximations to ground-state energies and wave functions. We shall apply it, in particular, to find approximations to the ground-state energy and wave functions for the He atom.
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2016
In this chapter we introduce some variational techniques, with the aim of obtaining further existence results for the periodic problem (P). We use some known results of differential calculus in normed vector spaces, which are collected in Appendix B.
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In this chapter we introduce some variational techniques, with the aim of obtaining further existence results for the periodic problem (P). We use some known results of differential calculus in normed vector spaces, which are collected in Appendix B.
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1976
Publisher Summary There is an equivalence between problems in the calculus of variations and problems involving partial differential equations (PDE). In particular, any PDE problem can be phrased in variational form. The variational form permits a useful alternative approach to the solution of the PDE problem.
GEORGE F. CARRIER, CARL E. PEARSON
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Publisher Summary There is an equivalence between problems in the calculus of variations and problems involving partial differential equations (PDE). In particular, any PDE problem can be phrased in variational form. The variational form permits a useful alternative approach to the solution of the PDE problem.
GEORGE F. CARRIER, CARL E. PEARSON
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