Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2019, Volume 22, Issue 1, pp. 27 - 59

.... This study aims to provide a survey of the recent relevant literature and findings in primary definitions, models, numerical methods and their applications...

60G22 | variable-order | fractional calculus | numerical methods | Primary 26A33 | 34A34 | 34A45 | fractional differential equations | Secondary 34A08 | 34K28 | 35R11 | 65M12 | applications | MATHEMATICS, APPLIED | CHAOTIC SYSTEM | DERIVATIVE MODEL | DISPERSION | SIMULATION | MATHEMATICS | ANOMALOUS DIFFUSION | SYNCHRONIZATION | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | COLLOCATION METHOD | STABILITY ANALYSIS | MECHANICAL PROPERTY EVOLUTION | Time dependence | Dynamic tests | Numerical analysis | Computer simulation | Dependent variables | Numerical methods | Differential equations | Mathematical models

60G22 | variable-order | fractional calculus | numerical methods | Primary 26A33 | 34A34 | 34A45 | fractional differential equations | Secondary 34A08 | 34K28 | 35R11 | 65M12 | applications | MATHEMATICS, APPLIED | CHAOTIC SYSTEM | DERIVATIVE MODEL | DISPERSION | SIMULATION | MATHEMATICS | ANOMALOUS DIFFUSION | SYNCHRONIZATION | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | COLLOCATION METHOD | STABILITY ANALYSIS | MECHANICAL PROPERTY EVOLUTION | Time dependence | Dynamic tests | Numerical analysis | Computer simulation | Dependent variables | Numerical methods | Differential equations | Mathematical models

Journal Article

1993, 1, ISBN 0849386365, 285

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of...

Mathematical models | Differential equations | Differential Equations | Differential equations-Mathematical models

Mathematical models | Differential equations | Differential Equations | Differential equations-Mathematical models

Book

3.
Scientific computing with Mathematica

: mathematical problems for ordinary differential equations

2001, Modeling and simulation in science, engineering, and technology, ISBN 0817642056, xiv, 270

Book

04/2017, 1st ed. 2017, Mathematical Engineering, ISBN 9783319552118, 261

.... Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics...

Engineering mathematics | Differential equations, partial | Differential equations, Partial

Engineering mathematics | Differential equations, partial | Differential equations, Partial

eBook

2017, Mathematical Engineering, ISBN 9783319552125

.... Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics...

Engineering | Partial differential equations | Mechanics, Applied | Mechanics | Mathematical models

Engineering | Partial differential equations | Mechanics, Applied | Mechanics | Mathematical models

Web Resource

2008, ISBN 9780470270851, xvi, 235

Book

2013, ISBN 1107023637, xix, 569

""Presents methods necessary for high accuracy computing of fluid flow and wave phenomena in single source format using unified spectral theory of...

Data processing | COMPUTERS / General | Fluid dynamics | Wave mechanics | Spectrum analysis | Physics

Data processing | COMPUTERS / General | Fluid dynamics | Wave mechanics | Spectrum analysis | Physics

Book

PLoS computational biology, ISSN 1553-7358, 2014, Volume 10, Issue 3, p. e1003359

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks...

REACTING SYSTEMS | LINEAR-SYSTEMS | STOCHASTIC SIMULATION | APPROXIMATION | FORMAT | MATRICES | BIOCHEMICAL RESEARCH METHODS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | GENE-EXPRESSION | DECOMPOSITION | BIOCHEMICAL REACTION NETWORKS | SOFTWARE PACKAGE | Computational Biology - methods | Algorithms | Stochastic Processes | Biochemistry - methods | Computer Simulation | Probability | Models, Statistical | Monte Carlo Method | Biological research | Mathematical research | Research | Tensors (Mathematics) | Computational biology | Biology, Experimental | Biology | Experiments | Methods | Linear algebra

REACTING SYSTEMS | LINEAR-SYSTEMS | STOCHASTIC SIMULATION | APPROXIMATION | FORMAT | MATRICES | BIOCHEMICAL RESEARCH METHODS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | GENE-EXPRESSION | DECOMPOSITION | BIOCHEMICAL REACTION NETWORKS | SOFTWARE PACKAGE | Computational Biology - methods | Algorithms | Stochastic Processes | Biochemistry - methods | Computer Simulation | Probability | Models, Statistical | Monte Carlo Method | Biological research | Mathematical research | Research | Tensors (Mathematics) | Computational biology | Biology, Experimental | Biology | Experiments | Methods | Linear algebra

Journal Article

2004, ISBN 9812388380, xvi, 401

Book

The Annals of applied probability, ISSN 1050-5164, 2015, Volume 25, Issue 6, pp. 3047 - 3094

Isotropic Gaussian random fields on the sphere are characterized by Karhunen–Loève expansions with respect to the spherical harmonic functions and the angular...

Karhunen-Loève expansion | Sample Hölder continuity | Stochastic partial differential equations | Kolmogorov-Chentsov theorem | Sample differentiability | Strong convergence rates | Isotropic random fields | Spherical harmonic functions | Spectral Galerkin methods | Gaussian random fields | sample Holder continuity | APPROXIMATION | PARTICLES | strong convergence rates | stochastic partial differential equations | LIGHT-SCATTERING | STATISTICS & PROBABILITY | sample differentiability | spectral Galerkin methods | isotropic random fields | Karhunen-Loeve expansion | spherical harmonic functions | 33C55 | 60G60 | Karhunen–Loève expansion | sample Hölder continuity | 41A25 | 65C30 | 60G17 | 60H15 | Kolmogorov–Chentsov theorem | 65N30 | 60G15 | 60H35 | Computational Mathematics | Beräkningsmatematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Karhunen-Loève expansion | Sample Hölder continuity | Stochastic partial differential equations | Kolmogorov-Chentsov theorem | Sample differentiability | Strong convergence rates | Isotropic random fields | Spherical harmonic functions | Spectral Galerkin methods | Gaussian random fields | sample Holder continuity | APPROXIMATION | PARTICLES | strong convergence rates | stochastic partial differential equations | LIGHT-SCATTERING | STATISTICS & PROBABILITY | sample differentiability | spectral Galerkin methods | isotropic random fields | Karhunen-Loeve expansion | spherical harmonic functions | 33C55 | 60G60 | Karhunen–Loève expansion | sample Hölder continuity | 41A25 | 65C30 | 60G17 | 60H15 | Kolmogorov–Chentsov theorem | 65N30 | 60G15 | 60H35 | Computational Mathematics | Beräkningsmatematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Journal Article

2001, Progress in nonlinear differential equations and their applications, ISBN 3764341106, Volume 45., xv, 341

Book

2005, 2nd ed., ISBN 1860945554, xiii, 416

Book

1989, Mechanical engineering, ISBN 9780824780487, Volume 66, x, 361

Book

2002, ISBN 0415272394, vii, 201

Book

Linear Algebra and Its Applications, ISSN 0024-3795, 06/2013, Volume 438, Issue 11, pp. 4204 - 4221

We consider a class of multilevel matrices arising, for example, from the discretization of linear diffusion operators in a d-dimensional hypercube. We derive...

Tensor Train (TT) and Quantized Tensor Train (QTT) formats | Curse of dimensionality | Low-rank representation | Diffusion operator | Semiseparable matrices | Quasi-separable matrices | MATHEMATICS, APPLIED | APPROXIMATION | TRAIN FORMAT | DECOMPOSITION | DIMENSIONS | MATRICES | EQUATION

Tensor Train (TT) and Quantized Tensor Train (QTT) formats | Curse of dimensionality | Low-rank representation | Diffusion operator | Semiseparable matrices | Quasi-separable matrices | MATHEMATICS, APPLIED | APPROXIMATION | TRAIN FORMAT | DECOMPOSITION | DIMENSIONS | MATRICES | EQUATION

Journal Article

2012, De Gruyter studies in mathematics, ISBN 3110258692, Volume 43, x, 291

Book

AIP Conference Proceedings, ISSN 0094-243X, 2012, Volume 1493, pp. 67 - 71

Conference Proceeding

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2013, Volume 51, Issue 3, pp. 2442 - 2471

This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic partial differential equation...

Distributed or boundary control | Linear parametric or stochastic PDE | Linear-quadratic optimal control | Analyticity | Elliptic or parabolic PDE | Generalized polynomial chaos approximation | MATHEMATICS, APPLIED | distributed or boundary control | TIME | linear parametric or stochastic PDE | EVOLUTION-EQUATIONS | elliptic or parabolic PDE | generalized polynomial chaos approximation | ADAPTIVE WAVELET METHODS | linear-quadratic optimal control | PARTIAL-DIFFERENTIAL-EQUATIONS | FINITE-ELEMENT APPROXIMATIONS | COEFFICIENTS | OPTIMIZATION | DIRICHLET BOUNDARY CONTROL | analyticity | MULTIGRID METHOD | AUTOMATION & CONTROL SYSTEMS | SCHEMES | Tensors | Constraints | Partial differential equations | Mathematical analysis | Mathematical models | Stochasticity | Galerkin methods | Adaptive control systems

Distributed or boundary control | Linear parametric or stochastic PDE | Linear-quadratic optimal control | Analyticity | Elliptic or parabolic PDE | Generalized polynomial chaos approximation | MATHEMATICS, APPLIED | distributed or boundary control | TIME | linear parametric or stochastic PDE | EVOLUTION-EQUATIONS | elliptic or parabolic PDE | generalized polynomial chaos approximation | ADAPTIVE WAVELET METHODS | linear-quadratic optimal control | PARTIAL-DIFFERENTIAL-EQUATIONS | FINITE-ELEMENT APPROXIMATIONS | COEFFICIENTS | OPTIMIZATION | DIRICHLET BOUNDARY CONTROL | analyticity | MULTIGRID METHOD | AUTOMATION & CONTROL SYSTEMS | SCHEMES | Tensors | Constraints | Partial differential equations | Mathematical analysis | Mathematical models | Stochasticity | Galerkin methods | Adaptive control systems

Journal Article

BIT Numerical Mathematics, ISSN 0006-3835, 2012, Volume 53, Issue 1, pp. 3 - 27

We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square...

Computational Mathematics and Numerical Analysis | Stochastic partial differential equations | Numeric Computing | Stochastic parabolic equation | Mathematics | 65C30 | 41A25 | Multilevel Monte Carlo | Mathematics, general | 65C05 | Multilevel approximations | 60H15 | Stochastic Finite Element Methods | 65N30 | 60H35 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SCHEME | MATHEMATICS, APPLIED | CONVERGENCE | Monte Carlo method | Analysis | Methods | Differential equations | Computational Mathematics | Beräkningsmatematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Computational Mathematics and Numerical Analysis | Stochastic partial differential equations | Numeric Computing | Stochastic parabolic equation | Mathematics | 65C30 | 41A25 | Multilevel Monte Carlo | Mathematics, general | 65C05 | Multilevel approximations | 60H15 | Stochastic Finite Element Methods | 65N30 | 60H35 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SCHEME | MATHEMATICS, APPLIED | CONVERGENCE | Monte Carlo method | Analysis | Methods | Differential equations | Computational Mathematics | Beräkningsmatematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Journal Article

1999, CRM series in mathematical physics, ISBN 0387988882, xxvi, 810

Book

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