Applied Mathematics and Computation, ISSN 0096-3003, 11/2014, Volume 247, pp. 30 - 46

In this paper, we derive an efficient spectral collocation algorithm to solve numerically the nonlinear complex generalized Zakharov system (GZS) subject to...

Nonlinear complex Zakharov-types equations | Pseudo-spectral scheme | Two-stage implicit Runge–Kutta | Jacobi–Gauss–Lobatto quadrature | Zakharov-types equations | Jacobi-Gauss-Lobatto quadrature | Runge-Kutta | Nonlinear complex | Two-stage implicit | Two-stage implicit Runge-Kutta | SPECTRAL METHOD | SCHEME | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | DIFFERENTIAL-EQUATIONS | WAVE SOLUTIONS | LOBATTO COLLOCATION METHOD | Accuracy | Algorithms | Approximation | Mathematical analysis | Nonlinearity | Boundary conditions | Mathematical models | Spectra

Nonlinear complex Zakharov-types equations | Pseudo-spectral scheme | Two-stage implicit Runge–Kutta | Jacobi–Gauss–Lobatto quadrature | Zakharov-types equations | Jacobi-Gauss-Lobatto quadrature | Runge-Kutta | Nonlinear complex | Two-stage implicit | Two-stage implicit Runge-Kutta | SPECTRAL METHOD | SCHEME | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | DIFFERENTIAL-EQUATIONS | WAVE SOLUTIONS | LOBATTO COLLOCATION METHOD | Accuracy | Algorithms | Approximation | Mathematical analysis | Nonlinearity | Boundary conditions | Mathematical models | Spectra

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 03/2014, Volume 261, pp. 244 - 255

A Jacobi–Gauss–Lobatto collocation (J-GL-C) method, used in combination with the implicit Runge–Kutta method of fourth order, is proposed as a numerical...

Gross–Pitaevskii equation | Nonlinear complex Schrödinger equations | Collocation method | Implicit Runge–Kutta method | Jacobi–Gauss–Lobatto quadrature | Implicit Runge-Kutta method | Jacobi-Gauss-Lobatto quadrature | Gross-Pitaevskii equation | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | 3RD | Nonlinear complex Schrodinger equations | ALGORITHMS | PHYSICS, MATHEMATICAL | VORTEX | SOLITON | Methods | Algorithms | Approximation | Mathematical analysis | Differential equations | Nonlinearity | Mathematical models | Runge-Kutta method | Schroedinger equation

Gross–Pitaevskii equation | Nonlinear complex Schrödinger equations | Collocation method | Implicit Runge–Kutta method | Jacobi–Gauss–Lobatto quadrature | Implicit Runge-Kutta method | Jacobi-Gauss-Lobatto quadrature | Gross-Pitaevskii equation | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | 3RD | Nonlinear complex Schrodinger equations | ALGORITHMS | PHYSICS, MATHEMATICAL | VORTEX | SOLITON | Methods | Algorithms | Approximation | Mathematical analysis | Differential equations | Nonlinearity | Mathematical models | Runge-Kutta method | Schroedinger equation

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2013, Volume 222, pp. 255 - 264

In this paper, we propose a new Jacobi–Gauss–Lobatto collocation method for solving the generalized Fitzhugh–Nagumo equation. The Jacobi–Gauss–Lobatto points...

Generalized Fitzhugh–Nagumo equation | Real Newell–Whitehead equation | Time-dependent Fitzhugh–Nagumo equation | Collocation method | Implicit Runge–Kutta method | Jacobi–Gauss–Lobatto quadrature | Implicit Runge-Kutta method | Generalized Fitzhugh-Nagumo equation | Jacobi-Gauss-Lobatto quadrature | Real Newell-Whitehead equation | Time-dependent Fitzhugh-Nagumo equation | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | NUMERICAL-SOLUTIONS | HEAT-TRANSFER | NON-LINEAR DIFFUSION | Methods | Algorithms

Generalized Fitzhugh–Nagumo equation | Real Newell–Whitehead equation | Time-dependent Fitzhugh–Nagumo equation | Collocation method | Implicit Runge–Kutta method | Jacobi–Gauss–Lobatto quadrature | Implicit Runge-Kutta method | Generalized Fitzhugh-Nagumo equation | Jacobi-Gauss-Lobatto quadrature | Real Newell-Whitehead equation | Time-dependent Fitzhugh-Nagumo equation | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | NUMERICAL-SOLUTIONS | HEAT-TRANSFER | NON-LINEAR DIFFUSION | Methods | Algorithms

Journal Article

4.
Full Text
On shifted Jacobi spectral approximations for solving fractional differential equations

Applied Mathematics and Computation, ISSN 0096-3003, 04/2013, Volume 219, Issue 15, pp. 8042 - 8056

► A new formula of fractional-order derivatives of shifted Jacobi polynomials is proved. ► A Jacobi spectral tau approximation for solving linear FDEs with...

Multi-term fractional differential equations | Shifted Jacobi polynomials | Jacobi–Gauss–Lobatto quadrature | Caputo derivative | Spectral methods | Nonlinear fractional initial value problems | Jacobi-Gauss-Lobatto quadrature | EXISTENCE | MATHEMATICS, APPLIED | TAU METHOD | OPERATIONAL MATRIX | ORDER | NUMERICAL-SOLUTION | COLLOCATION METHOD | COEFFICIENTS | EFFICIENT | Algorithms | Differential equations | Universities and colleges

Multi-term fractional differential equations | Shifted Jacobi polynomials | Jacobi–Gauss–Lobatto quadrature | Caputo derivative | Spectral methods | Nonlinear fractional initial value problems | Jacobi-Gauss-Lobatto quadrature | EXISTENCE | MATHEMATICS, APPLIED | TAU METHOD | OPERATIONAL MATRIX | ORDER | NUMERICAL-SOLUTION | COLLOCATION METHOD | COEFFICIENTS | EFFICIENT | Algorithms | Differential equations | Universities and colleges

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 02/2016, Volume 40, Issue 3, pp. 1703 - 1716

This paper extends the application of the spectral Jacobi–Gauss–Lobatto collocation (J-GL-C) method based on Gauss–Lobatto nodes to obtain semi-analytical...

Nonlinear reaction–diffusion equations | Collocation method | Jacobi–Gauss–Lobatto quadrature | Jacobi-Gauss-Lobatto quadrature | Nonlinear reaction-diffusion equations | TANH METHOD | APPROXIMATION | NAGUMO EQUATION | TIME | BURGERS-HUXLEY | TRAVELING-WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SPECTRAL GALERKIN METHOD | SOLITARY WAVE SOLUTIONS

Nonlinear reaction–diffusion equations | Collocation method | Jacobi–Gauss–Lobatto quadrature | Jacobi-Gauss-Lobatto quadrature | Nonlinear reaction-diffusion equations | TANH METHOD | APPROXIMATION | NAGUMO EQUATION | TIME | BURGERS-HUXLEY | TRAVELING-WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SPECTRAL GALERKIN METHOD | SOLITARY WAVE SOLUTIONS

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 53, Issue 9, pp. 1820 - 1832

This paper analyzes a method for solving the third- and fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov–Galerkin...

Jacobi polynomials | Petrov–Galerkin method | Jacobi–Jacobi Galerkin method | Jacobi collocation method | Jacobi–Gauss–Lobatto quadrature | Fast Fourier transform | Jacobi-Gauss-Lobatto quadrature | Jacobi-Jacobi Galerkin method | Petrov-Galerkin method | MATHEMATICS, APPLIED | ALGORITHMS | CHEBYSHEV COLLOCATION METHOD | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SPECTRAL METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATED FORMS

Jacobi polynomials | Petrov–Galerkin method | Jacobi–Jacobi Galerkin method | Jacobi collocation method | Jacobi–Gauss–Lobatto quadrature | Fast Fourier transform | Jacobi-Gauss-Lobatto quadrature | Jacobi-Jacobi Galerkin method | Petrov-Galerkin method | MATHEMATICS, APPLIED | ALGORITHMS | CHEBYSHEV COLLOCATION METHOD | POLYNOMIALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SPECTRAL METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATED FORMS

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2016, Volume 54, Issue 4, pp. 2081 - 2113

The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special...

Strongly normal point system | Chebyshev point | Jacobi-Gauss-Lobatto point | Polynomial interpolation | Limited regularity | Convergence rate | Gauss-Jacobi point | Peano kernel | NODES | MATHEMATICS, APPLIED | limited regularity | CLENSHAW-CURTIS QUADRATURE | strongly normal point system | ORDER | GAUSS-LEGENDRE | polynomial interpolation | WEIGHTS | ROOTS | COMPUTATION | convergence rate | POINTS | LAGRANGE INTERPOLATION

Strongly normal point system | Chebyshev point | Jacobi-Gauss-Lobatto point | Polynomial interpolation | Limited regularity | Convergence rate | Gauss-Jacobi point | Peano kernel | NODES | MATHEMATICS, APPLIED | limited regularity | CLENSHAW-CURTIS QUADRATURE | strongly normal point system | ORDER | GAUSS-LEGENDRE | polynomial interpolation | WEIGHTS | ROOTS | COMPUTATION | convergence rate | POINTS | LAGRANGE INTERPOLATION

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 05/2020, Volume 134, p. 109721

Functional differential equations have been widely used for modeling real-world phenomena in distinct areas of science. However, classical calculus can not...

Functional differential equation | Collocation method | Shifted fractional Jacobi-Gauss-Lobatto quadrature | Caputo fractional derivative | Shifted fractional Jacobi-Gauss-Radau quadrature

Functional differential equation | Collocation method | Shifted fractional Jacobi-Gauss-Lobatto quadrature | Caputo fractional derivative | Shifted fractional Jacobi-Gauss-Radau quadrature

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 4, pp. A1727 - A1751

The numerical computation of barycentric Hermite interpolation may suffer from devastating inaccuracies in the absence of overflow or underflow. In this paper,...

Hermite-Fejér interpolation | Jacobi polynomial | Chebyshev point | Gauss-Jacobi point | Barycentric | Jacobi-Gauss-Lobatto point | NODES | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | Hermite-Fejer interpolation | barycentric | GAUSS-LEGENDRE | QUADRATURE | WEIGHTS | ROOTS | COMPUTATION | POINTS

Hermite-Fejér interpolation | Jacobi polynomial | Chebyshev point | Gauss-Jacobi point | Barycentric | Jacobi-Gauss-Lobatto point | NODES | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | Hermite-Fejer interpolation | barycentric | GAUSS-LEGENDRE | QUADRATURE | WEIGHTS | ROOTS | COMPUTATION | POINTS

Journal Article

Romanian Journal of Physics, ISSN 1221-146X, 2014, Volume 59, Issue 3-4, pp. 247 - 264

A semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial...

Jacobi-Gauss-Lobatto quadrature | Nonlinear phenomena | Nonlinear coupled hyperbolic Klein-Gordon equations | Jacobi collocation method | TRAVELING-WAVE SOLUTIONS | SOLITONS | COLLOCATION METHOD | PHYSICS, MULTIDISCIPLINARY | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | MODEL

Jacobi-Gauss-Lobatto quadrature | Nonlinear phenomena | Nonlinear coupled hyperbolic Klein-Gordon equations | Jacobi collocation method | TRAVELING-WAVE SOLUTIONS | SOLITONS | COLLOCATION METHOD | PHYSICS, MULTIDISCIPLINARY | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | MODEL

Journal Article

COMPUTATIONAL MECHANICS, ISSN 0178-7675, 02/2020, Volume 65, Issue 2, pp. 475 - 486

In the present study, the radial basis functions (RBF) are combined with polynomial basis functions to approximate the fractional derivatives specifically. We...

MESHLESS METHOD | DIFFUSION EQUATIONS | Local support fields | POINT INTERPOLATION METHOD | Jacobi-Gauss-Lobatto quadratures | MULTI-TERM TIME | MODEL | Fractional derivatives | SPECTRAL METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Polynomial basis functions | Mixed RBF | FINITE-ELEMENT-METHOD

MESHLESS METHOD | DIFFUSION EQUATIONS | Local support fields | POINT INTERPOLATION METHOD | Jacobi-Gauss-Lobatto quadratures | MULTI-TERM TIME | MODEL | Fractional derivatives | SPECTRAL METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Polynomial basis functions | Mixed RBF | FINITE-ELEMENT-METHOD

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2012, Volume 2012, Issue 1, pp. 1 - 13

In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary...

collocation method | Jacobi-Gauss-Lobatto quadrature | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | three-point boundary conditions | fractional Langevin equation | shifted Jacobi polynomials | Partial Differential Equations | Shifted Jacobi polynomials | Three-point boundary conditions | Collocation method | Fractional Langevin equation | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS | OPERATIONAL MATRIX | CHEBYSHEV SPECTRAL METHOD | CONSTRUCTION | COEFFICIENTS | DERIVATIVES | Boundary value problems | Algebra | Collocation | Mathematical analysis | Collocation methods | Nonlinearity | Mathematical models | Derivatives

collocation method | Jacobi-Gauss-Lobatto quadrature | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | three-point boundary conditions | fractional Langevin equation | shifted Jacobi polynomials | Partial Differential Equations | Shifted Jacobi polynomials | Three-point boundary conditions | Collocation method | Fractional Langevin equation | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | MATHEMATICS | OPERATIONAL MATRIX | CHEBYSHEV SPECTRAL METHOD | CONSTRUCTION | COEFFICIENTS | DERIVATIVES | Boundary value problems | Algebra | Collocation | Mathematical analysis | Collocation methods | Nonlinearity | Mathematical models | Derivatives

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 2/2014, Volume 40, Issue 1, pp. 137 - 165

We present a novel predictor-corrector method, called Jacobian-predictor-corrector approach, for the numerical solutions of fractional ordinary differential...

Visualization | Computational Mathematics and Numerical Analysis | Jacobi-Gauss-Lobatto quadrature | Mathematical and Computational Biology | Mathematics | Computational Science and Engineering | Convergent order | 34A08 | 41A55 | Polynomial interpolation | Predictor-corrector | 65D05 | Computational cost | 65L20 | Mathematical Modeling and Industrial Mathematics | Jacobi-gauss-lobatto quadrature | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATIONS | INTEGRAL-EQUATIONS | VOLTERRA | Convergence (Mathematics) | Research | Mathematical research | Operator theory | Differential equations | Interpolation | Computation | Mathematical analysis | Mathematical models | Polynomials | Robustness | Computational efficiency

Visualization | Computational Mathematics and Numerical Analysis | Jacobi-Gauss-Lobatto quadrature | Mathematical and Computational Biology | Mathematics | Computational Science and Engineering | Convergent order | 34A08 | 41A55 | Polynomial interpolation | Predictor-corrector | 65D05 | Computational cost | 65L20 | Mathematical Modeling and Industrial Mathematics | Jacobi-gauss-lobatto quadrature | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATIONS | INTEGRAL-EQUATIONS | VOLTERRA | Convergence (Mathematics) | Research | Mathematical research | Operator theory | Differential equations | Interpolation | Computation | Mathematical analysis | Mathematical models | Polynomials | Robustness | Computational efficiency

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 6/2014, Volume 59, Issue 3, pp. 667 - 687

In this paper, we extend the study of superconvergence properties of Chebyshev-Gauss-type spectral interpolation in Zhang (SIAM J Numer Anal 50(5):2966–2985,...

Exponential convergence | Computational Mathematics and Numerical Analysis | 65N35 | Analytic functions | Theoretical, Mathematical and Computational Physics | Jacobi–Gauss–Radau and Jacobi–Gauss–Lobatto interpolations | Error remainder | Mathematics | Algorithms | 41A25 | 65M70 | Appl.Mathematics/Computational Methods of Engineering | Bernstein ellipse | 41A10 | 65E05 | Superconvergence points | 41A05 | Jacobi–Gauss | Jacobi-Gauss-Radau and Jacobi-Gauss-Lobatto interpolations | Jacobi-Gauss | MATHEMATICS, APPLIED | APPROXIMATION | EXPANSIONS | FOURIER | ANALYTIC-FUNCTIONS | EXPONENTIAL ACCURACY | COLLOCATION METHOD | GIBBS PHENOMENON | QUADRATURE | CONVERGENCE | ERROR-BOUNDS | Interpolation | Error analysis | Mathematical analysis | Constants | Mathematical models | Spectra | Convergence

Exponential convergence | Computational Mathematics and Numerical Analysis | 65N35 | Analytic functions | Theoretical, Mathematical and Computational Physics | Jacobi–Gauss–Radau and Jacobi–Gauss–Lobatto interpolations | Error remainder | Mathematics | Algorithms | 41A25 | 65M70 | Appl.Mathematics/Computational Methods of Engineering | Bernstein ellipse | 41A10 | 65E05 | Superconvergence points | 41A05 | Jacobi–Gauss | Jacobi-Gauss-Radau and Jacobi-Gauss-Lobatto interpolations | Jacobi-Gauss | MATHEMATICS, APPLIED | APPROXIMATION | EXPANSIONS | FOURIER | ANALYTIC-FUNCTIONS | EXPONENTIAL ACCURACY | COLLOCATION METHOD | GIBBS PHENOMENON | QUADRATURE | CONVERGENCE | ERROR-BOUNDS | Interpolation | Error analysis | Mathematical analysis | Constants | Mathematical models | Spectra | Convergence

Journal Article

15.
Numerical simulation of time variable fractional order mobile-immobile advection-dispersion model

Romanian Reports in Physics, ISSN 1221-1451, 09/2015, Volume 67, Issue 3, pp. 773 - 791

This paper reports a novel numerical technique for solving the time variable fractional order mobile-immobile advection-dispersion (TVFO-MIAD) model with the...

Jacobi-Gauss-Radau quadrature | Jacobi-Gauss-Lobatto quadrature | Coimbra fractional derivative | Collocation method | Mobile-immobile advection-dispersion equation | collocation method | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | DIFFUSION EQUATION | LOBATTO COLLOCATION METHOD | TRANSPORT | PARTIAL-DIFFERENTIAL-EQUATIONS | COEFFICIENTS | mobile-immobile advection-dispersion equation | CONVERGENCE | WAVE-EQUATION | OPERATORS | DERIVATIVES

Jacobi-Gauss-Radau quadrature | Jacobi-Gauss-Lobatto quadrature | Coimbra fractional derivative | Collocation method | Mobile-immobile advection-dispersion equation | collocation method | APPROXIMATION | PHYSICS, MULTIDISCIPLINARY | DIFFUSION EQUATION | LOBATTO COLLOCATION METHOD | TRANSPORT | PARTIAL-DIFFERENTIAL-EQUATIONS | COEFFICIENTS | mobile-immobile advection-dispersion equation | CONVERGENCE | WAVE-EQUATION | OPERATORS | DERIVATIVES

Journal Article

Journal of Computational and Nonlinear Dynamics, ISSN 1555-1415, 03/2015, Volume 10, Issue 2

A new spectral Jacobi-Gauss-Lobatto collocation (J-GL-C) method is developed and analyzed to solve numerically parabolic partial differential equations (PPDEs)...

collocation method | Jacobi-Gauss-Lobatto quadrature | implicit Runge-Kutta method | nonlocal boundary conditions | Neumann boundary conditions | Parabolic partial differential equations | SYSTEM | APPROXIMATION | STABILITY | parabolic partial differential equations | LOBATTO COLLOCATION METHOD | ENGINEERING, MECHANICAL | NUMERICAL-SOLUTION | MECHANICS | HEAT-EQUATION | SPECTRAL GALERKIN METHOD | SUBJECT | SCHEMES

collocation method | Jacobi-Gauss-Lobatto quadrature | implicit Runge-Kutta method | nonlocal boundary conditions | Neumann boundary conditions | Parabolic partial differential equations | SYSTEM | APPROXIMATION | STABILITY | parabolic partial differential equations | LOBATTO COLLOCATION METHOD | ENGINEERING, MECHANICAL | NUMERICAL-SOLUTION | MECHANICS | HEAT-EQUATION | SPECTRAL GALERKIN METHOD | SUBJECT | SCHEMES

Journal Article

Central European Journal of Physics, ISSN 1895-1082, 9/2014, Volume 12, Issue 9, pp. 637 - 653

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local...

collocation method | shifted Jacobi-Gauss-Lobatto quadrature | Environmental Physics | Physical Chemistry | non-local boundary conditions | system of differential equations | integral conservation condition | Geophysics/Geodesy | Biophysics and Biological Physics | Physics, general | Physics | PHYSICS, MULTIDISCIPLINARY | APPROXIMATIONS | DECOMPOSITION METHOD | BOUNDARY-VALUE-PROBLEMS | VARIATIONAL ITERATION METHOD | NUMERICAL-SOLUTION | PARTIAL-DIFFERENTIAL-EQUATIONS | PARABOLIC PROBLEM | SUBJECT

collocation method | shifted Jacobi-Gauss-Lobatto quadrature | Environmental Physics | Physical Chemistry | non-local boundary conditions | system of differential equations | integral conservation condition | Geophysics/Geodesy | Biophysics and Biological Physics | Physics, general | Physics | PHYSICS, MULTIDISCIPLINARY | APPROXIMATIONS | DECOMPOSITION METHOD | BOUNDARY-VALUE-PROBLEMS | VARIATIONAL ITERATION METHOD | NUMERICAL-SOLUTION | PARTIAL-DIFFERENTIAL-EQUATIONS | PARABOLIC PROBLEM | SUBJECT

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2013, Volume 2013, Issue 1, pp. 1 - 16

A Jacobi-Gauss-Lobatto collocation method is developed in this work to obtain spectral solutions for different versions of nonlinear time-dependent Phi-four...

Jacobi-Gauss-Lobatto quadrature | Ordinary Differential Equations | nonlinear time-dependent equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | nonlinear Phi-four equations | implicit Runge-Kutta method | Jacobi collocation method | Partial Differential Equations | Implicit Runge-Kutta method | Nonlinear Phi-four equations | Nonlinear time-dependent equations | MATHEMATICS | KLEIN-GORDON-SCHRODINGER | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | Usage | Schrodinger equation | Numerical analysis | Differential equations | Convergence (Mathematics) | Research

Jacobi-Gauss-Lobatto quadrature | Ordinary Differential Equations | nonlinear time-dependent equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | nonlinear Phi-four equations | implicit Runge-Kutta method | Jacobi collocation method | Partial Differential Equations | Implicit Runge-Kutta method | Nonlinear Phi-four equations | Nonlinear time-dependent equations | MATHEMATICS | KLEIN-GORDON-SCHRODINGER | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | Usage | Schrodinger equation | Numerical analysis | Differential equations | Convergence (Mathematics) | Research

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 8/2013, Volume 8, Issue 4, pp. 933 - 960

We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important...

Generalized Jacobi-Gauss-Lobatto interpolation | pseudospectral method | 65L60 | 65M70 | Mathematics, general | Mathematics | 41A05 | non-uniformly weighted Sobolev space | MATHEMATICS | HILBERT-SPACES | SPECTRAL-GALERKIN METHOD | 2ND-ORDER | TRIANGLE | SINGULAR DIFFERENTIAL-EQUATIONS | LINE | GEGENBAUER APPROXIMATION | Studies | Theorems | Algebra | Integral equations | Differential equations | Mathematical models | Interpolation | Sobolev space | Mathematical analysis | China | Derivatives

Generalized Jacobi-Gauss-Lobatto interpolation | pseudospectral method | 65L60 | 65M70 | Mathematics, general | Mathematics | 41A05 | non-uniformly weighted Sobolev space | MATHEMATICS | HILBERT-SPACES | SPECTRAL-GALERKIN METHOD | 2ND-ORDER | TRIANGLE | SINGULAR DIFFERENTIAL-EQUATIONS | LINE | GEGENBAUER APPROXIMATION | Studies | Theorems | Algebra | Integral equations | Differential equations | Mathematical models | Interpolation | Sobolev space | Mathematical analysis | China | Derivatives

Journal Article

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