Electronic journal of differential equations, ISSN 1072-6691, 01/2016, Volume 2016, Issue 6, pp. 1 - 8

In this article, by using the lower and upper solution method, we prove the existence of iterative solutions for a class of fractional initial value problem...

Fractional initial value problem | Existence of solutions | Lower and upper solution method | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | lower and upper solution method | existence of solutions

Fractional initial value problem | Existence of solutions | Lower and upper solution method | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | lower and upper solution method | existence of solutions

Journal Article

Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2017, Volume 42, pp. 675 - 681

â€¢We introduce a new norm that is convenient for the fractional and singular differential equations.â€¢The existence and uniqueness of initial value problems for...

Iterative method | Caputo fractional derivative | Fractional Langevin equation | Initial value problem | Existence and uniqueness | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | UNIQUENESS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Analysis | Numerical analysis | Differential equations

Iterative method | Caputo fractional derivative | Fractional Langevin equation | Initial value problem | Existence and uniqueness | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | UNIQUENESS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Analysis | Numerical analysis | Differential equations

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 09/2017, Volume 321, pp. 226 - 231

A new phase fitted Rungeâ€“Kutta pair of orders 8(7) which is a modification of a well known explicit Rungeâ€“Kutta pair for the integration of periodic initial...

Rungeâ€“Kutta | Numerical solution | Initial value problem | Variable step | Phase fitted | MATHEMATICS, APPLIED | NUMERICAL-INTEGRATION | Runge Kutta | INITIAL-VALUE PROBLEMS

Rungeâ€“Kutta | Numerical solution | Initial value problem | Variable step | Phase fitted | MATHEMATICS, APPLIED | NUMERICAL-INTEGRATION | Runge Kutta | INITIAL-VALUE PROBLEMS

Journal Article

Reviews of modern physics, ISSN 1539-0756, 2016, Volume 88, Issue 1

X-ray free-electron lasers (x-ray FELs) give us for the first time the possibility to explore structures and dynamical processes of atomic and molecular...

HIGH-GAIN REGIME | HARMONIC-GENERATION | STIMULATED-EMISSION | PHOTON STATISTICS | PHYSICS, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEM | COHERENCE PROPERTIES | EXTREME-ULTRAVIOLET | AMPLIFIED SPONTANEOUS-EMISSION | SINGLE-PASS | ULTRA-SHORT | Molecular structure | Free electron lasers | X-rays | Coherence | Mathematical models | Atomic structure | Dynamical systems | Single electrons

HIGH-GAIN REGIME | HARMONIC-GENERATION | STIMULATED-EMISSION | PHOTON STATISTICS | PHYSICS, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEM | COHERENCE PROPERTIES | EXTREME-ULTRAVIOLET | AMPLIFIED SPONTANEOUS-EMISSION | SINGLE-PASS | ULTRA-SHORT | Molecular structure | Free electron lasers | X-rays | Coherence | Mathematical models | Atomic structure | Dynamical systems | Single electrons

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8113, 02/2015, Volume 48, Issue 6, pp. 65204 - 20

We describe a method to construct well-posed initial value problems (IVPs) for not necessarily integrable equations on not necessarily simply connected...

Initial value problem | Integrable | Quad-graph | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | quad-graph | initial value problem | integrable | Construction | Initial value problems | Well posed problems | Mathematical analysis

Initial value problem | Integrable | Quad-graph | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | quad-graph | initial value problem | integrable | Construction | Initial value problems | Well posed problems | Mathematical analysis

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 2011, Volume 62, Issue 3, pp. 1591 - 1601

We develop properties of the Laplace Transform in a discrete, fractional calculus setting, giving a precise treatment to convergence along the way. The end...

Exponential order | Convolution | Taylor monomial | Discrete fractional calculus | Laplace transform | Fractional initial value problem | MATHEMATICS, APPLIED | Calculus | Initial value problems | Mathematical models | Laplace transforms | Mathematical analysis | Convergence

Exponential order | Convolution | Taylor monomial | Discrete fractional calculus | Laplace transform | Fractional initial value problem | MATHEMATICS, APPLIED | Calculus | Initial value problems | Mathematical models | Laplace transforms | Mathematical analysis | Convergence

Journal Article

Computers & mathematics with applications (1987), ISSN 0898-1221, 07/2016, Volume 72, Issue 1, pp. 64 - 75

This paper considers the existence and uniqueness of the global smooth solution for the initial value problem of generalized Zakharov equations in dimension...

Global solutions | Initial value problem | Generalized Zakharov equations | SYSTEM | MATHEMATICS, APPLIED | WELL-POSEDNESS | KUZNETSOV EQUATION | Integrals | Mathematical analysis | Uniqueness | Initial value problems | Mathematical models | Estimates | Galerkin methods

Global solutions | Initial value problem | Generalized Zakharov equations | SYSTEM | MATHEMATICS, APPLIED | WELL-POSEDNESS | KUZNETSOV EQUATION | Integrals | Mathematical analysis | Uniqueness | Initial value problems | Mathematical models | Estimates | Galerkin methods

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2019, p. 112500

Journal Article

Living Reviews in Relativity, ISSN 2367-3613, 12/2012, Volume 15, Issue 1, pp. 1 - 99

I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic...

Cosmology | Astrophysics and Astroparticles | Classical and Quantum Gravitation, Relativity Theory | Physics | GRAVITATIONAL-WAVE-FORMS | PARTIAL-DIFFERENTIAL-EQUATIONS | LATE-TIME BEHAVIOR | BRANS-DICKE THEORY | CAUCHY-CHARACTERISTIC EXTRACTION | NUMERICAL RELATIVITY | INITIAL-VALUE-PROBLEM | BLACK-HOLE | ABSORBING BOUNDARY-CONDITIONS | VACUUM FIELD-EQUATIONS | PHYSICS, PARTICLES & FIELDS | Feasibility studies | Review | Numerical methods | Characteristic initial value problem | Numerical relativity

Cosmology | Astrophysics and Astroparticles | Classical and Quantum Gravitation, Relativity Theory | Physics | GRAVITATIONAL-WAVE-FORMS | PARTIAL-DIFFERENTIAL-EQUATIONS | LATE-TIME BEHAVIOR | BRANS-DICKE THEORY | CAUCHY-CHARACTERISTIC EXTRACTION | NUMERICAL RELATIVITY | INITIAL-VALUE-PROBLEM | BLACK-HOLE | ABSORBING BOUNDARY-CONDITIONS | VACUUM FIELD-EQUATIONS | PHYSICS, PARTICLES & FIELDS | Feasibility studies | Review | Numerical methods | Characteristic initial value problem | Numerical relativity

Journal Article

Numerical Algorithms, ISSN 1017-1398, 8/2016, Volume 72, Issue 4, pp. 1089 - 1102

A new optimized two-step hybrid block method for the numerical integration of general second-order initial value problems is presented. The method considers...

Algorithms | Algebra | General second-order initial-value problem | Numerical Analysis | Computer Science | Numeric Computing | Optimization criterium | Theory of Computation | Intra-step nodal points | MSC 65L05 | Hybrid block method | Y''=F(X,Y,Y') | MATHEMATICS, APPLIED | MULTISTEP METHODS | NYSTROM METHODS | Computer science | International trade | Analysis | Methods

Algorithms | Algebra | General second-order initial-value problem | Numerical Analysis | Computer Science | Numeric Computing | Optimization criterium | Theory of Computation | Intra-step nodal points | MSC 65L05 | Hybrid block method | Y''=F(X,Y,Y') | MATHEMATICS, APPLIED | MULTISTEP METHODS | NYSTROM METHODS | Computer science | International trade | Analysis | Methods

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2010, Volume 367, Issue 1, pp. 260 - 272

In this paper, we shall discuss the properties of the well-known Mittagâ€“Leffler function, and consider the existence and uniqueness of solution of the initial...

Fractional differential equation | Riemannâ€“Liouville sequential fractional derivatives | Initial value problem | Upper solution and lower solution | Riemann-Liouville sequential fractional derivatives | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | INTEGRAL-EQUATIONS | UNIQUENESS | MATHEMATICS | ORDER | MONOTONE ITERATIVE TECHNIQUE | 1ST-ORDER

Fractional differential equation | Riemannâ€“Liouville sequential fractional derivatives | Initial value problem | Upper solution and lower solution | Riemann-Liouville sequential fractional derivatives | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | INTEGRAL-EQUATIONS | UNIQUENESS | MATHEMATICS | ORDER | MONOTONE ITERATIVE TECHNIQUE | 1ST-ORDER

Journal Article

Journal of functional analysis, ISSN 0022-1236, 01/2016, Volume 270, Issue 2, pp. 718 - 747

On any closed Riemannian manifold of dimension greater than 7, we construct examples of background physical coefficients for which the Einsteinâ€“Lichnerowicz...

Finite-dimensional reduction | Initial-value problem in General Relativity | Blow-up theory | Initial-value problem in general relativity | MATHEMATICS | FIELD LICHNEROWICZ EQUATIONS | STABILITY | Relativity | YAMABE | SIGN-CHANGING SOLUTIONS | BLOW-UP PHENOMENA | Initial-value problem in General

Finite-dimensional reduction | Initial-value problem in General Relativity | Blow-up theory | Initial-value problem in general relativity | MATHEMATICS | FIELD LICHNEROWICZ EQUATIONS | STABILITY | Relativity | YAMABE | SIGN-CHANGING SOLUTIONS | BLOW-UP PHENOMENA | Initial-value problem in General

Journal Article

Journal of differential geometry, ISSN 0022-040X, 09/2018, Volume 110, Issue 1, pp. 73 - 133

We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future asymptotically flat null cone, and show...

MATHEMATICS | INITIAL-VALUE PROBLEM

MATHEMATICS | INITIAL-VALUE PROBLEM

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 251, Issue 4, pp. 902 - 917

In this paper we study the random-data initial value problem of the Navierâ€“Stokes equations in
L
2
(
T
3
)
. By using the randomization approach recently...

Navierâ€“Stokes equations | Randomization | Initial value problem | Navier-Stokes equations | EXISTENCE | MATHEMATICS | INITIAL VALUE-PROBLEM | WEAK SOLUTIONS | Fluid dynamics

Navierâ€“Stokes equations | Randomization | Initial value problem | Navier-Stokes equations | EXISTENCE | MATHEMATICS | INITIAL VALUE-PROBLEM | WEAK SOLUTIONS | Fluid dynamics

Journal Article

Journal of Physics: Conference Series, ISSN 1742-6588, 12/2018, Volume 1139, Issue 1

Conference Proceeding

Journal of Difference Equations and Applications, ISSN 1023-6198, 03/2018, Volume 24, Issue 3, pp. 305 - 343

We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function...

green function | initial value problem | Chebyshev functions | Chebyshev polynomials | Second order difference equations | MATHEMATICS, APPLIED | CHEBYSHEV | Functions (mathematics) | Chebyshev approximation | Ice | Polynomials | Green's functions | Difference equations | Problemes de valor inicial | ClassificaciÃ³ AMS | Polinomis | MatemÃ tiques i estadÃstica | Initial value problems | 12 Field theory and polynomials | Ã€rees temÃ tiques de la UPC

green function | initial value problem | Chebyshev functions | Chebyshev polynomials | Second order difference equations | MATHEMATICS, APPLIED | CHEBYSHEV | Functions (mathematics) | Chebyshev approximation | Ice | Polynomials | Green's functions | Difference equations | Problemes de valor inicial | ClassificaciÃ³ AMS | Polinomis | MatemÃ tiques i estadÃstica | Initial value problems | 12 Field theory and polynomials | Ã€rees temÃ tiques de la UPC

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2016, Volume 49, Issue 44, p. 445202

We describe a seemingly un-noticed feature of the text-book Maxwell-Lorentz system of classical electrodynamics which challenges its formulation in terms of an...

classical electrodynamics | initial value problem | singular light fronts | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | PHYSICS, MATHEMATICAL | 2-BODY PROBLEM

classical electrodynamics | initial value problem | singular light fronts | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | PHYSICS, MATHEMATICAL | 2-BODY PROBLEM

Journal Article

AIAA Journal, ISSN 0001-1452, 08/2011, Volume 49, Issue 8, pp. 1647 - 1657

The discrete spectrum of disturbances in high-speed boundary layers is discussed with emphasis on singularities caused by synchronization of the normal modes....

FLAT-PLATE | ACOUSTIC DISTURBANCES | FLOWS | ENGINEERING, AEROSPACE | RECEPTIVITY | INITIAL-VALUE PROBLEM | Mechanical properties | Numerical analysis | Research | Singularities (Mathematics) | Boundary layer | Stability | Terminology | High speed | Synchronism | Instability | Spectra | Synchronization

FLAT-PLATE | ACOUSTIC DISTURBANCES | FLOWS | ENGINEERING, AEROSPACE | RECEPTIVITY | INITIAL-VALUE PROBLEM | Mechanical properties | Numerical analysis | Research | Singularities (Mathematics) | Boundary layer | Stability | Terminology | High speed | Synchronism | Instability | Spectra | Synchronization

Journal Article

Annual review of fluid mechanics, ISSN 1545-4479, 2011, Volume 43, Issue 1, pp. 319 - 352

This article reviews linear instability analysis of flows over or through complex two-dimensional (2D) and 3D geometries. In the three decades since it first...

two-dimensional and three-dimensional eigenvalue and initial value problem | BiGlobal and TriGlobal instability | inhomogeneous flows in complex domains | flow control | modal and nonmodal instability | 3-DIMENSIONAL INSTABILITIES | PHYSICS, FLUIDS & PLASMAS | BOUNDARY-LAYER-FLOW | OPTIMAL DISTURBANCES | SEPARATION-BUBBLES | MECHANICS | NAVIER-STOKES EQUATIONS | STABILITY ANALYSIS | FINITE-ELEMENT | TURBULENT-FLOW | CONVECTIVE INSTABILITY | NUMERICAL-SIMULATION | Eigenvalues | Differential equations | Research | Stability | Fluid dynamics | Instability | Initial value problems | Two dimensional | Aerospace engineering | Three dimensional

two-dimensional and three-dimensional eigenvalue and initial value problem | BiGlobal and TriGlobal instability | inhomogeneous flows in complex domains | flow control | modal and nonmodal instability | 3-DIMENSIONAL INSTABILITIES | PHYSICS, FLUIDS & PLASMAS | BOUNDARY-LAYER-FLOW | OPTIMAL DISTURBANCES | SEPARATION-BUBBLES | MECHANICS | NAVIER-STOKES EQUATIONS | STABILITY ANALYSIS | FINITE-ELEMENT | TURBULENT-FLOW | CONVECTIVE INSTABILITY | NUMERICAL-SIMULATION | Eigenvalues | Differential equations | Research | Stability | Fluid dynamics | Instability | Initial value problems | Two dimensional | Aerospace engineering | Three dimensional

Journal Article