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Título : Numerical Methods for Laplace Transform Inversion Tipo de documento: documento electrónico Autores: Alan M. Cohen ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2007 Colección: Numerical Methods and Algorithms, ISSN 1571-5698 num. 5 Número de páginas: XIV, 252 p. 25 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-68855-8 Idioma : Inglés (eng) Palabras clave: Mathematics Integral transforms Operational calculus Applied mathematics Engineering Transforms, Calculus Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Audience This book is intended for engineers, scientists, mathematicians, statisticians and financial planners Nota de contenido: Basic Results -- Inversion Formulae and Practical Results -- The Method of Series Expansion -- Quadrature Methods -- Rational Approximation Methods -- The Method of Talbot -- Methods based on the Post-Widder Inversion Formula -- The Method of Regularization -- Survey Results -- Applications En línea: http://dx.doi.org/10.1007/978-0-387-68855-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34510 Numerical Methods for Laplace Transform Inversion [documento electrónico] / Alan M. Cohen ; SpringerLink (Online service) . - Boston, MA : Springer US, 2007 . - XIV, 252 p. 25 illus : online resource. - (Numerical Methods and Algorithms, ISSN 1571-5698; 5) .
ISBN : 978-0-387-68855-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral transforms Operational calculus Applied mathematics Engineering Transforms, Calculus Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Audience This book is intended for engineers, scientists, mathematicians, statisticians and financial planners Nota de contenido: Basic Results -- Inversion Formulae and Practical Results -- The Method of Series Expansion -- Quadrature Methods -- Rational Approximation Methods -- The Method of Talbot -- Methods based on the Post-Widder Inversion Formula -- The Method of Regularization -- Survey Results -- Applications En línea: http://dx.doi.org/10.1007/978-0-387-68855-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34510 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Algebraic Analysis of Differential Equations / SpringerLink (Online service) ; Takashi Aoki ; Hideyuki Majima ; Yoshitsugu Takei ; Nobuyuki Tose (2008)
Título : Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Takashi Aoki ; Hideyuki Majima ; Yoshitsugu Takei ; Nobuyuki Tose Editorial: Tokyo : Springer Japan Fecha de publicación: 2008 Número de páginas: XVII, 352 p Il.: online resource ISBN/ISSN/DL: 978-4-431-73240-2 Idioma : Inglés (eng) Palabras clave: Mathematics Integral transforms Operational calculus Differential equations Partial differential Special functions Transforms, Calculus Ordinary Equations Functions Clasificación: 51 Matemáticas Nota de contenido: The work of T. Kawai -- Publications of Professor Takahiro Kawai -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on exact WKB analysis -- Contributed papers -- Virtual turning points — A gift of microlocal analysis to the exact WKB analysis -- Regular sequences associated with the Noumi-Yamada equations with a large parameter -- Ghost busting: Making sense of non-Hermitian Hamiltonians -- Vanishing of the logarithmic trace of generalized Szegö projectors -- Nonlinear Stokes phenomena in first or second order differential equations -- Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation -- Exact WKB analysis near a simple turning point -- The Borel transform -- On the use of Z-transforms in the summation of transseries for partial differential equations -- Some dynamical aspects of Painlevé VI -- An algebraic representation for correlation functions in integrable spin chains -- Inverse image of D-modules and quasi-b-functions -- The hypoelliptic Laplacian of J.-M. Bismut -- Commuting differential operators with regular singularities -- The behaviors of singular solutions of some partial differential equations in the complex domain -- Observations on the JWKB treatment of the quadratic barrier -- A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map -- Spectral instability for non-selfadjoint operators -- Boundary and lens rigidity, tensor tomography and analytic microlocal analysis -- Coupling of two partial differential equations and its application -- Instanton-type formal solutions for the first Painlevé hierarchy -- From exact-WKB toward singular quantum perturbation theory II -- WKB analysis and Poincaré theorem for vector fields En línea: http://dx.doi.org/10.1007/978-4-431-73240-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34431 Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai [documento electrónico] / SpringerLink (Online service) ; Takashi Aoki ; Hideyuki Majima ; Yoshitsugu Takei ; Nobuyuki Tose . - Tokyo : Springer Japan, 2008 . - XVII, 352 p : online resource.
ISBN : 978-4-431-73240-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral transforms Operational calculus Differential equations Partial differential Special functions Transforms, Calculus Ordinary Equations Functions Clasificación: 51 Matemáticas Nota de contenido: The work of T. Kawai -- Publications of Professor Takahiro Kawai -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on hyperfunction theory and microlocal analysis -- The work of T. Kawai on exact WKB analysis -- Contributed papers -- Virtual turning points — A gift of microlocal analysis to the exact WKB analysis -- Regular sequences associated with the Noumi-Yamada equations with a large parameter -- Ghost busting: Making sense of non-Hermitian Hamiltonians -- Vanishing of the logarithmic trace of generalized Szegö projectors -- Nonlinear Stokes phenomena in first or second order differential equations -- Reconstruction of inclusions for the inverse boundary value problem for non-stationary heat equation -- Exact WKB analysis near a simple turning point -- The Borel transform -- On the use of Z-transforms in the summation of transseries for partial differential equations -- Some dynamical aspects of Painlevé VI -- An algebraic representation for correlation functions in integrable spin chains -- Inverse image of D-modules and quasi-b-functions -- The hypoelliptic Laplacian of J.-M. Bismut -- Commuting differential operators with regular singularities -- The behaviors of singular solutions of some partial differential equations in the complex domain -- Observations on the JWKB treatment of the quadratic barrier -- A role of virtual turning points and new Stokes curves in Stokes geometry of the quantum Hénon map -- Spectral instability for non-selfadjoint operators -- Boundary and lens rigidity, tensor tomography and analytic microlocal analysis -- Coupling of two partial differential equations and its application -- Instanton-type formal solutions for the first Painlevé hierarchy -- From exact-WKB toward singular quantum perturbation theory II -- WKB analysis and Poincaré theorem for vector fields En línea: http://dx.doi.org/10.1007/978-4-431-73240-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34431 Ejemplares
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Título : Approximation by Multivariate Singular Integrals Tipo de documento: documento electrónico Autores: George A. Anastassiou ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: SpringerBriefs in Mathematics, ISSN 2191-8198 Número de páginas: X, 79 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-0589-4 Idioma : Inglés (eng) Palabras clave: Mathematics Integral transforms Operational calculus Partial differential equations Probabilities Transforms, Calculus Differential Equations Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables. Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level En línea: http://dx.doi.org/10.1007/978-1-4614-0589-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33229 Approximation by Multivariate Singular Integrals [documento electrónico] / George A. Anastassiou ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - X, 79 p : online resource. - (SpringerBriefs in Mathematics, ISSN 2191-8198) .
ISBN : 978-1-4614-0589-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral transforms Operational calculus Partial differential equations Probabilities Transforms, Calculus Differential Equations Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last chapter, which includes many examples, presents a related Korovkin type approximation theorem for functions of two variables. Relevant background information and motivation is included in this exposition, and as a result this book can be used as supplementary text for several advanced courses. The results presented apply to many areas of pure and applied mathematics, such a mathematical analysis, probability, statistics and partial differential equations. This book is appropriate for researchers and selected seminars at the graduate level En línea: http://dx.doi.org/10.1007/978-1-4614-0589-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33229 Ejemplares
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Título : Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach Tipo de documento: documento electrónico Autores: Victor D. Didenko ; SpringerLink (Online service) ; Silbermann, Bernd Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: XII, 306 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8751-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Integral equations transforms Operational calculus Operator theory Partial differential Numerical analysis Theory Analysis Equations Transforms, Calculus Differential Clasificación: 51 Matemáticas Resumen: Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive – i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous Nota de contenido: Complex and Real Algebras -- Approximation of Additive Integral Operators on Smooth Curves -- Approximation Methods for the Riemann-Hilbert Problem -- Piecewise Smooth and Open Contours -- Approximation Methods for the Muskhelishvili Equation -- Numerical Examples En línea: http://dx.doi.org/10.1007/978-3-7643-8751-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34416 Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach [documento electrónico] / Victor D. Didenko ; SpringerLink (Online service) ; Silbermann, Bernd . - Basel : Birkhäuser Basel, 2008 . - XII, 306 p : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-7643-8751-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Integral equations transforms Operational calculus Operator theory Partial differential Numerical analysis Theory Analysis Equations Transforms, Calculus Differential Clasificación: 51 Matemáticas Resumen: Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive – i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous Nota de contenido: Complex and Real Algebras -- Approximation of Additive Integral Operators on Smooth Curves -- Approximation Methods for the Riemann-Hilbert Problem -- Piecewise Smooth and Open Contours -- Approximation Methods for the Muskhelishvili Equation -- Numerical Examples En línea: http://dx.doi.org/10.1007/978-3-7643-8751-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34416 Ejemplares
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Título : Fractional Differentiation Inequalities Tipo de documento: documento electrónico Autores: George A. Anastassiou ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Número de páginas: XIV, 686 p Il.: online resource ISBN/ISSN/DL: 978-0-387-98128-4 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Integral transforms Operational calculus Differential equations Partial differential Ordinary Equations Analysis Transforms, Calculus Clasificación: 51 Matemáticas Resumen: Fractional differentiation inequalities are by themselves an important area of research. They have many applications in pure and applied mathematics and many other applied sciences. One of the most important applications is in establishing the uniqueness of a solution in fractional differential equations and systems and in fractional partial differential equations. They also provide upper bounds to the solutions of the above equations. In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful Nota de contenido: Opial#x2013;Type Inequalities for Functions and Their Ordinary and Canavati Fractional Derivatives -- Canavati Fractional Opial#x2013;Type Inequalities and Fractional Differential Equations -- Riemann#x2014;Liouville Opial#x2014;type Inequalities for Fractional Derivatives -- Opial#x2013;type #x2013;Inequalities for Riemann#x2014;Liouville Fractional Derivatives -- Opial#x2013;Type Inequalities Involving Canavati Fractional Derivatives of Two Functions and Applications -- Opial#x2013;Type Inequalities for Riemann#x2014;Liouville Fractional Derivatives of Two Functions with Applications -- Canavati Fractional Opial#x2013;Type Inequalities for Several Functions and Applications -- Riemann#x2014;Liouville Fractional#x2013;Opial Type Inequalities for Several Functions and Applications -- Converse Canavati Fractional Opial#x2013;Type Inequalities for Several Functions -- Converse Riemann#x2014;Liouville Fractional Opial#x2013;Type Inequalities for Several Functions -- Multivariate Canavati Fractional Taylor Formula -- Multivariate Caputo Fractional Taylor Formula -- Canavati Fractional Multivariate Opial#x2013;Type Inequalities on Spherical Shells -- Riemann#x2014;Liouville Fractional Multivariate Opial#x2013;type inequalities over a spherical shell -- Caputo Fractional Multivariate Opial#x2013;Type Inequalities over a Spherical Shell -- Poincar#x00E9;#x2013;Type Fractional Inequalities -- Various Sobolev#x2013;Type Fractional Inequalities -- General Hilbert#x2014;Pachpatte#x2013;Type Integral Inequalities -- General Multivariate Hilbert#x2014;Pachpatte#x2013;Type Integral Inequalities -- Other Hilbert#x2014;Pachpatte#x2013;Type Fractional Integral Inequalities -- Canavati Fractional and Other Approximation of Csiszar#x2019;s #x2013;Divergence -- Caputo and Riemann#x2014;Liouville Fractional Approximation of Csiszar#x2019;s #x2013;Divergence -- Canavati Fractional Ostrowski#x2013;Type Inequalities -- Multivariate Canavati Fractional Ostrowski#x2013;Type Inequalities -- Caputo Fractional Ostrowski#x2013;Type Inequalities En línea: http://dx.doi.org/10.1007/978-0-387-98128-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33928 Fractional Differentiation Inequalities [documento electrónico] / George A. Anastassiou ; SpringerLink (Online service) . - New York, NY : Springer New York, 2009 . - XIV, 686 p : online resource.
ISBN : 978-0-387-98128-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Integral transforms Operational calculus Differential equations Partial differential Ordinary Equations Analysis Transforms, Calculus Clasificación: 51 Matemáticas Resumen: Fractional differentiation inequalities are by themselves an important area of research. They have many applications in pure and applied mathematics and many other applied sciences. One of the most important applications is in establishing the uniqueness of a solution in fractional differential equations and systems and in fractional partial differential equations. They also provide upper bounds to the solutions of the above equations. In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined. This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful Nota de contenido: Opial#x2013;Type Inequalities for Functions and Their Ordinary and Canavati Fractional Derivatives -- Canavati Fractional Opial#x2013;Type Inequalities and Fractional Differential Equations -- Riemann#x2014;Liouville Opial#x2014;type Inequalities for Fractional Derivatives -- Opial#x2013;type #x2013;Inequalities for Riemann#x2014;Liouville Fractional Derivatives -- Opial#x2013;Type Inequalities Involving Canavati Fractional Derivatives of Two Functions and Applications -- Opial#x2013;Type Inequalities for Riemann#x2014;Liouville Fractional Derivatives of Two Functions with Applications -- Canavati Fractional Opial#x2013;Type Inequalities for Several Functions and Applications -- Riemann#x2014;Liouville Fractional#x2013;Opial Type Inequalities for Several Functions and Applications -- Converse Canavati Fractional Opial#x2013;Type Inequalities for Several Functions -- Converse Riemann#x2014;Liouville Fractional Opial#x2013;Type Inequalities for Several Functions -- Multivariate Canavati Fractional Taylor Formula -- Multivariate Caputo Fractional Taylor Formula -- Canavati Fractional Multivariate Opial#x2013;Type Inequalities on Spherical Shells -- Riemann#x2014;Liouville Fractional Multivariate Opial#x2013;type inequalities over a spherical shell -- Caputo Fractional Multivariate Opial#x2013;Type Inequalities over a Spherical Shell -- Poincar#x00E9;#x2013;Type Fractional Inequalities -- Various Sobolev#x2013;Type Fractional Inequalities -- General Hilbert#x2014;Pachpatte#x2013;Type Integral Inequalities -- General Multivariate Hilbert#x2014;Pachpatte#x2013;Type Integral Inequalities -- Other Hilbert#x2014;Pachpatte#x2013;Type Fractional Integral Inequalities -- Canavati Fractional and Other Approximation of Csiszar#x2019;s #x2013;Divergence -- Caputo and Riemann#x2014;Liouville Fractional Approximation of Csiszar#x2019;s #x2013;Divergence -- Canavati Fractional Ostrowski#x2013;Type Inequalities -- Multivariate Canavati Fractional Ostrowski#x2013;Type Inequalities -- Caputo Fractional Ostrowski#x2013;Type Inequalities En línea: http://dx.doi.org/10.1007/978-0-387-98128-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33928 Ejemplares
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