Special meshes and higher-order schemes for singularly perturbed boundary value problems.
Vulanović, Relja (2001)
Novi Sad Journal of Mathematics
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Vulanović, Relja (2001)
Novi Sad Journal of Mathematics
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Jaroslav Doležal, Jiří Fidler (1979)
Kybernetika
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Khattri, Sanjay Kumar (2006)
Differential Equations & Nonlinear Mechanics
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Calzada, Maria E. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Joseph W. Jerome (1985)
Numerische Mathematik
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Faker Ben Belgacem, Michel Fournié, Nabil Gmati, Faten Jelassi (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical...
P. Barral, P. Quintela, M. T. Sánchez (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez–Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper,...
Jonas Koko (2004)
International Journal of Applied Mathematics and Computer Science
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Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each...