1.
Classical methods in ordinary differential equations

: with applications to boundary value problems

2012, Graduate studies in mathematics, ISBN 0821846949, Volume 129, xvii, 373

Book

2009, Princeton mathematical series, ISBN 0691137773, Volume 48, xvi, 677

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial...

Differential equations, Elliptic | Quasiconformal mappings | Mathematics

Differential equations, Elliptic | Quasiconformal mappings | Mathematics

Book

Complex variables and elliptic equations, ISSN 1747-6933, 2006

Journal

2017, EMS tracts in mathematics, ISBN 9783037191675, Volume 26., xxiv, 472 pages

Winner of the 2016 EMS Monograph Award! Complex Monge-Ampère equations have been one of the most powerful tools in Kähler geometry since Aubin and Yau's...

Monge-Ampère equations | Pluripotential theory | Plurisubharmonic functions

Monge-Ampère equations | Pluripotential theory | Plurisubharmonic functions

Book

2011, Graduate studies in mathematics, ISBN 0821853236, Volume 121, xii, 313

"Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in...

Minimal surfaces

Minimal surfaces

Book

Communications in Theoretical Physics, ISSN 0253-6102, 11/2012, Volume 58, Issue 5, pp. 623 - 630

In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville...

exact solutions | fractional partial differential equations | fractional complex transformation | (G′/G)-expansion method | (G '/G)-expansion method | EXISTENCE | ORDER | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | STABILITY | PERTURBATION TECHNIQUE

exact solutions | fractional partial differential equations | fractional complex transformation | (G′/G)-expansion method | (G '/G)-expansion method | EXISTENCE | ORDER | TRAVELING-WAVE SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | STABILITY | PERTURBATION TECHNIQUE

Journal Article

2016, Second edition., Graduate studies in mathematics, ISBN 1470409860, Volume 175., xviii, 453 pages

Book

2018, Lecture Notes in Mathematics, ISBN 9783319740416, Volume 2211

eBook

2011, Courant lecture notes in mathematics, ISBN 0821872869, Volume 22, xi, 149

Book

2006, 5th ed., ISBN 0125637381

Book

Thermal Science, ISSN 0354-9836, 2012, Volume 16, Issue 2, pp. 331 - 334

A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential...

Modified riemann-Liouville derivative | Time-fractional heat conduction equation | Fractional KdV equation | time-fractional heat conduction equation | THERMODYNAMICS | COMPLEX TRANSFORM | modified Riemann-Liouville derivative | fractional KdV equation | time-fractional Heat Conduction Equation

Modified riemann-Liouville derivative | Time-fractional heat conduction equation | Fractional KdV equation | time-fractional heat conduction equation | THERMODYNAMICS | COMPLEX TRANSFORM | modified Riemann-Liouville derivative | fractional KdV equation | time-fractional Heat Conduction Equation

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2015, Volume 38, Issue 13, pp. 2779 - 2784

In this article, the sub‐equation method is presented for finding the exact solutions of a nonlinear fractional partial differential equations. For this, the...

subclass34A08 | 83C15 | exact solutions | fractional complex transform | time fractional differential equations | 35R11 | sub‐equation method | Sub-equation method | Subclass34A08 | Fractional complex transform | Time fractional differential equations | Exact solutions | sub-equation method | MATHEMATICS, APPLIED | Transformations (mathematics) | Partial differential equations | Mathematical analysis | Differential equations | Nonlinearity | Mathematical models | Derivatives

subclass34A08 | 83C15 | exact solutions | fractional complex transform | time fractional differential equations | 35R11 | sub‐equation method | Sub-equation method | Subclass34A08 | Fractional complex transform | Time fractional differential equations | Exact solutions | sub-equation method | MATHEMATICS, APPLIED | Transformations (mathematics) | Partial differential equations | Mathematical analysis | Differential equations | Nonlinearity | Mathematical models | Derivatives

Journal Article

2013, Undergraduate Texts in Mathematics, ISBN 3319020986, 652

eBook

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2010, Volume 199, Issue 23, pp. 1603 - 1626

Over the past years, model reduction techniques have become a necessary path for the reduction of computational requirements in the numerical simulation of...

Evolution problems | Generalized Spectral Decomposition | Separation of variables | Model reduction | Proper Orthogonal Decomposition (POD) | Proper Generalized Decomposition (PGD) | SPECTRAL DECOMPOSITION | COMPLEX FLUIDS | PARABOLIC-PROBLEMS | COMPUTATIONAL STRATEGY | ORTHOGONAL DECOMPOSITION | PARAMETERS | ALGORITHMS | SOLVERS | HOMOGENIZATION | FAMILY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Construction | Computer simulation | Partial differential equations | Mathematical analysis | Decomposition | Mathematical models | Representations | Numerical Analysis | Mathematics

Evolution problems | Generalized Spectral Decomposition | Separation of variables | Model reduction | Proper Orthogonal Decomposition (POD) | Proper Generalized Decomposition (PGD) | SPECTRAL DECOMPOSITION | COMPLEX FLUIDS | PARABOLIC-PROBLEMS | COMPUTATIONAL STRATEGY | ORTHOGONAL DECOMPOSITION | PARAMETERS | ALGORITHMS | SOLVERS | HOMOGENIZATION | FAMILY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Construction | Computer simulation | Partial differential equations | Mathematical analysis | Decomposition | Mathematical models | Representations | Numerical Analysis | Mathematics

Journal Article

2014, Springer monographs in mathematics, ISBN 3642388701, xviii, 307 pages

This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in...

Differential equations, Linear | Galois theory | Differential algebra | Topological algebras

Differential equations, Linear | Galois theory | Differential algebra | Topological algebras

Book

Journal of Non-Newtonian Fluid Mechanics, ISSN 0377-0257, 2006, Volume 139, Issue 3, pp. 153 - 176

Kinetic theory models involving the Fokker–Planck equation can be accurately discretized using a mesh support (finite elements, finite differences, finite...

Numerical modeling | Separation of variables | Kinetic theory | Model reduction | Complex fluids | Multidimensional problems | multidimensional problems | MECHANICS | complex fluids | REDUCTION | FINITELY EXTENSIBLE DUMBBELLS | model reduction | SYSTEMS | kinetic theory | separation of variables | FOKKER-PLANCK EQUATIONS | numerical modeling | Mechanics | Engineering Sciences | Fluids mechanics

Numerical modeling | Separation of variables | Kinetic theory | Model reduction | Complex fluids | Multidimensional problems | multidimensional problems | MECHANICS | complex fluids | REDUCTION | FINITELY EXTENSIBLE DUMBBELLS | model reduction | SYSTEMS | kinetic theory | separation of variables | FOKKER-PLANCK EQUATIONS | numerical modeling | Mechanics | Engineering Sciences | Fluids mechanics

Journal Article

Chinese Physics B, ISSN 1674-1056, 11/2012, Volume 21, Issue 11, pp. 110204 - 1-110204-7

In this article, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential...

fractional calculus | improved (G'=G)-expansion function method | modified Riemann-Liouville derivative | complex transformation | ORDER | PHYSICS, MULTIDISCIPLINARY | improved (G '/G)-expansion function method | TRANSFORM | Foams | Mathematical analysis | Exact solutions | Differential equations | Nonlinearity | Evolution | Transformations | Derivatives

fractional calculus | improved (G'=G)-expansion function method | modified Riemann-Liouville derivative | complex transformation | ORDER | PHYSICS, MULTIDISCIPLINARY | improved (G '/G)-expansion function method | TRANSFORM | Foams | Mathematical analysis | Exact solutions | Differential equations | Nonlinearity | Evolution | Transformations | Derivatives

Journal Article

Neurocomputing, ISSN 0925-2312, 11/2018, Volume 317, pp. 28 - 41

In this paper, we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how...

Advection | Deep neural networks | Partial differential equations | Diffusion | Complex geometries | SEQUENCES | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | DERIVATIVES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Mathematics | Naturvetenskap | Natural Sciences | Beräkningsmatematik | Computational Mathematics | Matematik

Advection | Deep neural networks | Partial differential equations | Diffusion | Complex geometries | SEQUENCES | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | DERIVATIVES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Mathematics | Naturvetenskap | Natural Sciences | Beräkningsmatematik | Computational Mathematics | Matematik

Journal Article

1990, 4. Aufl., A series of modern surveys in mathematics, ISBN 0387520228, Volume 34, xiv, 244

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began...

Differential equations, Nonlinear | Hamiltonian systems | Calculus of variations

Differential equations, Nonlinear | Hamiltonian systems | Calculus of variations

Book

SIAM Review, ISSN 0036-1445, 3/2014, Volume 56, Issue 1, pp. 159 - 186

The classical methods for solving initial-boundary-value problems for linear partial differential equations with constant coefficients rely on separation of...

Greens theorem | Integrands | Partial differential equations | Heat equation | Constant coefficients | Mathematical integrals | Boundary conditions | Fourier transformations | Real lines | EDUCATION | Mathematical expressions | Complex analysis | Evolution equations | complex analysis | MATHEMATICS, APPLIED | partial differential equations | TRANSFORM METHOD | evolution equations | Differential equations, Linear | Boundary value problems | Differential equations, Partial | Analysis | Tests, problems and exercises | Studies | Complex systems | Intervals | Integrals | Mathematical analysis | Transforms | Cases (containers)

Greens theorem | Integrands | Partial differential equations | Heat equation | Constant coefficients | Mathematical integrals | Boundary conditions | Fourier transformations | Real lines | EDUCATION | Mathematical expressions | Complex analysis | Evolution equations | complex analysis | MATHEMATICS, APPLIED | partial differential equations | TRANSFORM METHOD | evolution equations | Differential equations, Linear | Boundary value problems | Differential equations, Partial | Analysis | Tests, problems and exercises | Studies | Complex systems | Intervals | Integrals | Mathematical analysis | Transforms | Cases (containers)

Journal Article

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