2015, Mathematical surveys and monographs, ISBN 1470425580, Volume 207, xii, 479

Book

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2016, Volume 39, Issue 10, pp. 2461 - 2476

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear...

time‐fractional partial differential equations (TFPDEs) | time‐fractional sine‐Gordon equations | boundary elements method (BEM) | time‐fractional telegraph equation | radial basis functions (RBFs) | boundary integral equation method | time‐fractional Fokker–Planck equations | time‐fractional Klein–Gordon equations | dual reciprocity boundary elements method (DRBEM) | time-fractional telegraph equation | time-fractional partial differential equations (TFPDEs) | time-fractional sine-Gordon equations | time-fractional Fokker–Planck equations | time-fractional Klein–Gordon equations | CONVECTION FLOW | MATHEMATICS, APPLIED | ELEMENT-METHOD | TELEGRAPH EQUATION | time-fractional Fokker-Planck equations | SUB-DIFFUSION EQUATION | HIGH-ORDER | SPACE | SCHEME | NUMERICAL-SOLUTION | DRBEM SOLUTION | time-fractional Klein-Gordon equations | SINE-GORDON | Methods | Differential equations | Partial differential equations | Reciprocity | Integral equations | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Boundaries

time‐fractional partial differential equations (TFPDEs) | time‐fractional sine‐Gordon equations | boundary elements method (BEM) | time‐fractional telegraph equation | radial basis functions (RBFs) | boundary integral equation method | time‐fractional Fokker–Planck equations | time‐fractional Klein–Gordon equations | dual reciprocity boundary elements method (DRBEM) | time-fractional telegraph equation | time-fractional partial differential equations (TFPDEs) | time-fractional sine-Gordon equations | time-fractional Fokker–Planck equations | time-fractional Klein–Gordon equations | CONVECTION FLOW | MATHEMATICS, APPLIED | ELEMENT-METHOD | TELEGRAPH EQUATION | time-fractional Fokker-Planck equations | SUB-DIFFUSION EQUATION | HIGH-ORDER | SPACE | SCHEME | NUMERICAL-SOLUTION | DRBEM SOLUTION | time-fractional Klein-Gordon equations | SINE-GORDON | Methods | Differential equations | Partial differential equations | Reciprocity | Integral equations | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Boundaries

Journal Article

2012, 3rd ed., World Scientific series in contemporary chemical physics, ISBN 9789814355667, Volume 27, xxii, 827

Book

2007, 3rd ed., North-Holland personal library., ISBN 9780444529357, xvi, 463

The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of...

Statistical methods | Chemistry, Physical and theoretical | Stochastic processes | Statistical physics | Chemistry, Physical and theoretical - Statistical methods

Statistical methods | Chemistry, Physical and theoretical | Stochastic processes | Statistical physics | Chemistry, Physical and theoretical - Statistical methods

Book

2005, Springer complexity, ISBN 3540212647, xii, 404

Book

1989, 2nd ed. --, Springer series in synergetics, ISBN 0387504982, Volume 18, xiv, 472

Book

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2014, Volume 52, Issue 6, pp. 2599 - 2622

In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear...

Hypergeometric functions | Error rates | Approximation | Porous materials | Numerical methods | Differential equations | Reaction diffusion equations | Legendre polynomials | Spectral methods | Finite difference methods | Riesz space fractional reaction-diffusion equation | Fractional FitzHugh-Nagumo model | Alternating direction implicit method | Legendre spectral method | Stability and convergence | FOKKER-PLANCK EQUATION | stability and convergence | MATHEMATICS, APPLIED | fractional FitzHugh-Nagumo model | STABILITY | GALERKIN METHOD | FINITE-DIFFERENCE METHOD | SUBDIFFUSION EQUATION | alternating direction implicit method | NUMERICAL APPROXIMATION | ANOMALOUS DIFFUSION | SOURCE-TERM | CONVERGENCE | ADVECTION-DISPERSION | Nodular iron | Nonlinearity | Mathematical models | Reaction-diffusion equations | Two dimensional | Galerkin methods | Convergence

Hypergeometric functions | Error rates | Approximation | Porous materials | Numerical methods | Differential equations | Reaction diffusion equations | Legendre polynomials | Spectral methods | Finite difference methods | Riesz space fractional reaction-diffusion equation | Fractional FitzHugh-Nagumo model | Alternating direction implicit method | Legendre spectral method | Stability and convergence | FOKKER-PLANCK EQUATION | stability and convergence | MATHEMATICS, APPLIED | fractional FitzHugh-Nagumo model | STABILITY | GALERKIN METHOD | FINITE-DIFFERENCE METHOD | SUBDIFFUSION EQUATION | alternating direction implicit method | NUMERICAL APPROXIMATION | ANOMALOUS DIFFUSION | SOURCE-TERM | CONVERGENCE | ADVECTION-DISPERSION | Nodular iron | Nonlinearity | Mathematical models | Reaction-diffusion equations | Two dimensional | Galerkin methods | Convergence

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1315 - 1324

In the standard continuous time random walk the initial state is taken as a non-equilibrium state, in which the random walking particle has just arrived at a...

Fokker–Planck equations | Fractional diffusion | Continuous time random walks | MATHEMATICS, APPLIED | Fokker-Planck equations | DIFFUSION

Fokker–Planck equations | Fractional diffusion | Continuous time random walks | MATHEMATICS, APPLIED | Fokker-Planck equations | DIFFUSION

Journal Article

Journal of the Physical Society of Japan, ISSN 0031-9015, 2006, Volume 75, Issue 8, pp. 082001 - 1"-"082001-39

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9...

NMR | Stochastic Liouville equation | quantum Fokker-Planck equation | 2D spectroscopy | Quantum Fokker-Planck equation

NMR | Stochastic Liouville equation | quantum Fokker-Planck equation | 2D spectroscopy | Quantum Fokker-Planck equation

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2008, Volume 47, Issue 1, pp. 204 - 226

We develop the finite element method for the numerical resolution of the space and time fractional Fokker–Planck equation, which is an effective tool for...

Finite element method | Error rates | Approximation | Abstract spaces | Random walk | Fokker Planck equation | Differential equations | Boundary conditions | Calculus | Stability | Lovy flights | Fractional fokkor-planck equation | Convergence | Levy flights | ANOMALOUS DIFFUSION | ORDER | MATHEMATICS, APPLIED | finite element method | convergence | RANDOM-WALKS | fractional Fokker-Planck equation | DERIVATIVES | stability

Finite element method | Error rates | Approximation | Abstract spaces | Random walk | Fokker Planck equation | Differential equations | Boundary conditions | Calculus | Stability | Lovy flights | Fractional fokkor-planck equation | Convergence | Levy flights | ANOMALOUS DIFFUSION | ORDER | MATHEMATICS, APPLIED | finite element method | convergence | RANDOM-WALKS | fractional Fokker-Planck equation | DERIVATIVES | stability

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2018, Volume 354, pp. 242 - 268

Solving the Fokker–Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional...

Gaussian mixture | Hybrid method | Fokker–Planck equation | High-dimensional non-Gaussian PDFs | Conditional Gaussian structures | Intermittency | REGRESSION-MODELS | ENSEMBLE KALMAN FILTER | UNCERTAINTY QUANTIFICATION | Fokker-Planck equation | PHYSICS, MATHEMATICAL | RARE EVENTS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MADDEN-JULIAN OSCILLATION | QUANTIFYING UNCERTAINTY | SYSTEMS | ERROR | EXTREME EVENTS | Turbulence | Analysis | Algorithms

Gaussian mixture | Hybrid method | Fokker–Planck equation | High-dimensional non-Gaussian PDFs | Conditional Gaussian structures | Intermittency | REGRESSION-MODELS | ENSEMBLE KALMAN FILTER | UNCERTAINTY QUANTIFICATION | Fokker-Planck equation | PHYSICS, MATHEMATICAL | RARE EVENTS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MADDEN-JULIAN OSCILLATION | QUANTIFYING UNCERTAINTY | SYSTEMS | ERROR | EXTREME EVENTS | Turbulence | Analysis | Algorithms

Journal Article

12.
Full Text
A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 05/2019, Volume 522, pp. 158 - 166

We consider the one-dimensional bistable Fokker–Planck equation proposed by Polotto et al. (2018), with specific drift and diffusion coefficients so as to...

Eigenvalues | Bistable | Fokker–Planck | Pseudospectral | Schrödinger equation | PROFILES | STATES | THERMALIZATION | PHYSICS, MULTIDISCIPLINARY | RELAXATION | ENERGY LANDSCAPES | Fokker-Planck | WKB | QUADRATURE DISCRETIZATION METHOD | Schrodinger equation | DIFFUSION | Protein folding

Eigenvalues | Bistable | Fokker–Planck | Pseudospectral | Schrödinger equation | PROFILES | STATES | THERMALIZATION | PHYSICS, MULTIDISCIPLINARY | RELAXATION | ENERGY LANDSCAPES | Fokker-Planck | WKB | QUADRATURE DISCRETIZATION METHOD | Schrodinger equation | DIFFUSION | Protein folding

Journal Article

13.
Full Text
Analytical approximation to the multidimensional Fokker–Planck equation with steady state

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2019, Volume 52, Issue 8, p. 85002

The Fokker-Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions...

Fokker–Planck equation | Mean reversion | Stochastic processes | mean reversion | PHYSICS, MULTIDISCIPLINARY | STATISTICS | DIFFUSION | Fokker-Planck equation | stochastic processes | PHYSICS, MATHEMATICAL

Fokker–Planck equation | Mean reversion | Stochastic processes | mean reversion | PHYSICS, MULTIDISCIPLINARY | STATISTICS | DIFFUSION | Fokker-Planck equation | stochastic processes | PHYSICS, MATHEMATICAL

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1243 - 1261

Latterly, many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, to a series of...

Time-fractional partial differential equations | Reproducing kernel Hilbert space method | Neumann boundary conditions | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher’s, and Newell–Whitehead) equations | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher's, and Newell–Whitehead) equations | FOKKER-PLANCK EQUATION | SYSTEM | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker-Planck, Fisher's, and Newell-Whitehead)equations | MATHEMATICS, APPLIED | VOLTERRA INTEGRAL-EQUATIONS | TURNING-POINT PROBLEMS | SUBDIFFUSION EQUATION | NUMERICAL ALGORITHM | SCHEMES | Methods | Numerical analysis | Differential equations

Time-fractional partial differential equations | Reproducing kernel Hilbert space method | Neumann boundary conditions | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher’s, and Newell–Whitehead) equations | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher's, and Newell–Whitehead) equations | FOKKER-PLANCK EQUATION | SYSTEM | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker-Planck, Fisher's, and Newell-Whitehead)equations | MATHEMATICS, APPLIED | VOLTERRA INTEGRAL-EQUATIONS | TURNING-POINT PROBLEMS | SUBDIFFUSION EQUATION | NUMERICAL ALGORITHM | SCHEMES | Methods | Numerical analysis | Differential equations

Journal Article

European Journal of Control, ISSN 0947-3580, 11/2019, Volume 50, pp. 20 - 29

•We obtained and proved a potential and effective approach to control the entropy of complex processes described by the stochastic Gompertz model.•To obtain...

Shannon entropy | Fokker–Planck equation | Entropy stability | Stochastic Gompertz model | THERAPY | GROWTH | Fokker-Planck equation | MODEL | AUTOMATION & CONTROL SYSTEMS | Controllers | Systems stability | Economic models | Population growth | Statistical analysis | Stochastic processes | Entropy | Maximum likelihood method | Probability density functions | Time dependence | Chemotherapy | Algorithms | Morphology | Control stability | Control theory | Stochastic models

Shannon entropy | Fokker–Planck equation | Entropy stability | Stochastic Gompertz model | THERAPY | GROWTH | Fokker-Planck equation | MODEL | AUTOMATION & CONTROL SYSTEMS | Controllers | Systems stability | Economic models | Population growth | Statistical analysis | Stochastic processes | Entropy | Maximum likelihood method | Probability density functions | Time dependence | Chemotherapy | Algorithms | Morphology | Control stability | Control theory | Stochastic models

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 03/2018, Volume 320, pp. 302 - 318

In the paper, we consider a time-space spectral method to get the numerical solution of time-space fractional Fokker–Planck initial-boundary value problem. The...

L–M method | Time-space fractional Fokker–Planck equation | Time-space spectral method | Stability and convergence | MATHEMATICS, APPLIED | PARAMETER-ESTIMATION | APPROXIMATION | NUMERICAL ALGORITHMS | L-M method | TRANSPORT | Time-space fractional Fokker-Planck equation | DIFFUSION-EQUATIONS | KINETICS | ADVECTION-DISPERSION EQUATIONS | DYNAMICAL MODELS | BIOLOGICAL-SYSTEMS

L–M method | Time-space fractional Fokker–Planck equation | Time-space spectral method | Stability and convergence | MATHEMATICS, APPLIED | PARAMETER-ESTIMATION | APPROXIMATION | NUMERICAL ALGORITHMS | L-M method | TRANSPORT | Time-space fractional Fokker-Planck equation | DIFFUSION-EQUATIONS | KINETICS | ADVECTION-DISPERSION EQUATIONS | DYNAMICAL MODELS | BIOLOGICAL-SYSTEMS

Journal Article