Nonlinear Volterra integral equation of the second kind and biorthogonal systems.
Berenguer, M.I., Gámez, D., Garralda-Guillem, A.I., Pérez, M.C.Serrano (2010)
Abstract and Applied Analysis
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Displaying similar documents to “Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation.”
Nonlinear Volterra integral equation of the second kind and biorthogonal systems.
Biorthogonal systems approximating the solution of the nonlinear Volterra integro-differential equation.
Berenguer, M.I., Garralda-Guillem, A.I., Galán, M.Ruiz (2010)
Fixed Point Theory and Applications [electronic only]
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Analytical techniques for a numerical solution of the linear Volterra integral equation of the second kind.
Berenguer, M.I., Gámez, D., Garralda-Guillem, A.I., Galán, M.Ruiz, Pérez, M.C.Serrano (2009)
Abstract and Applied Analysis
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Biorthogonal systems and bases in Banach space (Preliminary note)
Jiří Vaníček (1960)
Commentationes Mathematicae Universitatis Carolinae
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Block-by-block method for solving nonlinear Volterra-Fredholm integral equation.
Badr, Abdallah A. (2010)
Mathematical Problems in Engineering
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Numerical solvability of a class of Volterra-Hammerstein integral equations with noncompact kernels.
Hadizadeh, M., Mohamadsohi, M. (2005)
Journal of Applied Mathematics
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A simple proof of two theorems concerning bases of
G. Schechtman (1978-1979)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces.
Bica, Alexandru, Căuş, Vasile Aurel, Mureşan, Sorin (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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On uncountable unconditional bases in Banach spaces
Lech Drewnowski (1988)
Studia Mathematica
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Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
Alexandre Janon, Maëlle Nodet, Clémentine Prieur (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.
Equivalence of Bases in Non-archimedean Banach Spaces
P.K. Jain, N.M. Kapoor (1980)
Publications de l'Institut Mathématique
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Properties of lush spaces and applications to Banach spaces with numerical index 1
Kostyantyn Boyko, Vladimir Kadets, Miguel Martín, Javier Merí (2009)
Studia Mathematica
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The concept of lushness, introduced recently, is a Banach space property, which ensures that the space has numerical index 1. We prove that for Asplund spaces lushness is actually equivalent to having numerical index 1. We prove that every separable Banach space containing an isomorphic copy of c₀ can be renormed equivalently to be lush, and thus to have numerical index 1. The rest of the paper is devoted to the study of lushness just as a property of Banach spaces. We prove that lushness...
Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions
Nemati, S., Lima, P., Ordokhani, Y.
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A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is tested on a number of problems and numerical results are given.