Applied Mathematical Modelling, ISSN 0307-904X, 10/2018, Volume 62, pp. 629 - 637

•Fractional dual-phase-lag model is proposed to analyze the diffusion in comb model.•Solutions are obtained analytically with Laplace and Fourier...

Constitutive equation | Comb model | Relaxation parameter | Anomalous diffusion | Fractional derivative | CELLS | FOURIER HEAT-CONDUCTION | CATTANEO-CHRISTOV FLUX | PROCESSED MEAT | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | EQUATION

Constitutive equation | Comb model | Relaxation parameter | Anomalous diffusion | Fractional derivative | CELLS | FOURIER HEAT-CONDUCTION | CATTANEO-CHRISTOV FLUX | PROCESSED MEAT | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | EQUATION

Journal Article

Waves in Random and Complex Media, ISSN 1745-5030, 03/2020, pp. 1 - 24

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 9/2016, Volume 54, Issue 8, pp. 1696 - 1727

A new embedded symmetric six-step method with vanished phase-lag and its first, second, third and fourth derivatives is obtained for the first time in the...

Explicit methods | Phase-fitted | Schrödinger equation | Multistage methods | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | 4-STEP METHODS | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

Explicit methods | Phase-fitted | Schrödinger equation | Multistage methods | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | 4-STEP METHODS | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 05/2016, Volume 54, Issue 5, pp. 1159 - 1186

In this paper, we introduce for the first time in the literature a family of embedded explicit symmetric six-step methods. The family of the proposed methods...

Interval of periodicity | P-stability | Explicit methods | Multistep methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Multistage methods | Schrödinger equation | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | HIGH-ORDER | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | SYMMETRIC MULTISTEP METHODS | Analysis

Interval of periodicity | P-stability | Explicit methods | Multistep methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Multistage methods | Schrödinger equation | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | HIGH-ORDER | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | SYMMETRIC MULTISTEP METHODS | Analysis

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 4/2016, Volume 54, Issue 4, pp. 1010 - 1040

In this paper we develop a new implicit eighth algebraic order symmetric six-step method. For this method we request for the first time in the literature...

65L05 | Explicit methods | Phase-fitted | Schrödinger equation | Multistage methods | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | HYBRID EXPLICIT METHODS | RUNGE-KUTTA METHODS | HIGH-ORDER | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | Usage | Chemistry, Physical and theoretical | Analysis

65L05 | Explicit methods | Phase-fitted | Schrödinger equation | Multistage methods | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | HYBRID EXPLICIT METHODS | RUNGE-KUTTA METHODS | HIGH-ORDER | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | Usage | Chemistry, Physical and theoretical | Analysis

Journal Article

International Journal of Heat and Mass Transfer, ISSN 0017-9310, 02/2015, Volume 81, pp. 347 - 354

For effective medical treatment processes, to understand the evolution of thermal responses in the biological tissues is important. Therefore, a non-Fourier...

Dual phase lag | Laser irradiation | Thermal damage | Non-Fourier | BEHAVIOR | MODEL | DAMAGE | ENGINEERING, MECHANICAL | TRANSPORT | MECHANICS | THERMODYNAMICS | CONDUCTION | BIO-HEAT TRANSFER | LASER-IRRADIATED TISSUE | Evolution | Analysis | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Biological | Phase lag | Damage | Heat transfer

Dual phase lag | Laser irradiation | Thermal damage | Non-Fourier | BEHAVIOR | MODEL | DAMAGE | ENGINEERING, MECHANICAL | TRANSPORT | MECHANICS | THERMODYNAMICS | CONDUCTION | BIO-HEAT TRANSFER | LASER-IRRADIATED TISSUE | Evolution | Analysis | Mathematical analysis | Nonlinearity | Mathematical models | Derivatives | Biological | Phase lag | Damage | Heat transfer

Journal Article

Numerical Algorithms, ISSN 1017-1398, 02/2019, Volume 80, Issue 2, pp. 557 - 593

A new family of three-stage two-step methods are presented in this paper. These methods are of algebraic order 12 and have an important P-stability property....

Ordinary differential equations | P-stable | Phase-lag | Phase-fitting | Multiderivative methods | Schrödinger equation | MATHEMATICS, APPLIED | KUTTA-NYSTROM METHOD | FITTED OBRECHKOFF METHODS | INITIAL-VALUE PROBLEMS | CHOICE | 1ST | Schrodinger equation | INTEGRATION | HIGH-ORDER METHOD | FREQUENCY | SUPER-IMPLICIT METHODS | SYMMETRIC MULTISTEP METHODS

Ordinary differential equations | P-stable | Phase-lag | Phase-fitting | Multiderivative methods | Schrödinger equation | MATHEMATICS, APPLIED | KUTTA-NYSTROM METHOD | FITTED OBRECHKOFF METHODS | INITIAL-VALUE PROBLEMS | CHOICE | 1ST | Schrodinger equation | INTEGRATION | HIGH-ORDER METHOD | FREQUENCY | SUPER-IMPLICIT METHODS | SYMMETRIC MULTISTEP METHODS

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2016, Volume 13, Issue 6, pp. 5177 - 5194

In this paper, we will develop a four-stage high algebraic order symmetric two-step method with vanished phase-lag and its first up to the fourth derivative....

initial value problems | hybrid | Primary 65L05 | multistep | Mathematics, general | Mathematics | derivative of the phase-lag | Phase-lag | oscillating solution | symmetric | Schrödinger equation | ORBITAL PROBLEMS | MATHEMATICS, APPLIED | INITIAL-VALUE-PROBLEMS | MATHEMATICS | Schrodinger equation | LAG | MULTISTEP METHODS | INTEGRATION | SCATTERING

initial value problems | hybrid | Primary 65L05 | multistep | Mathematics, general | Mathematics | derivative of the phase-lag | Phase-lag | oscillating solution | symmetric | Schrödinger equation | ORBITAL PROBLEMS | MATHEMATICS, APPLIED | INITIAL-VALUE-PROBLEMS | MATHEMATICS | Schrodinger equation | LAG | MULTISTEP METHODS | INTEGRATION | SCATTERING

Journal Article

Journal of Computational and Theoretical Nanoscience, ISSN 1546-1955, 04/2014, Volume 11, Issue 4, pp. 987 - 992

The present investigation deals with the thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a cylindrical cavity. The...

Anisotropic | Generalized Thermoelasticity | Finite Element Method | Fiber-Reinforced | Three-Phase Lag | PHYSICS, CONDENSED MATTER | MAGNETOELASTIC SHEAR-WAVES | SURFACE | PROPAGATION | Anisotropy | Mathematical analysis | Fiber composites | Reinforcement | Holes | Mathematical models | Nanostructure | Derivatives

Anisotropic | Generalized Thermoelasticity | Finite Element Method | Fiber-Reinforced | Three-Phase Lag | PHYSICS, CONDENSED MATTER | MAGNETOELASTIC SHEAR-WAVES | SURFACE | PROPAGATION | Anisotropy | Mathematical analysis | Fiber composites | Reinforcement | Holes | Mathematical models | Nanostructure | Derivatives

Journal Article

Journal of Thermal Stresses, ISSN 0149-5739, 11/2019, Volume 42, Issue 11, pp. 1415 - 1431

In the application of pulsed laser heating, such as the laser hardening of metallic surfaces, the conduction limited process is the dominant mechanism during...

Non-Gaussian laser pulse | Laplace Transform | memory dependent derivative | Finite Fourier transform | three-phase-lag thermoelastic model | microscale beam | THERMOELASTICITY | STRAIN GRADIENT PLASTICITY | MECHANICS | THERMODYNAMICS | DYNAMICS | HALF-SPACE | HARDNESS | PLATE | Kernel functions | Three phase | Derivatives | Pulsed lasers | Workpieces | Time dependence | Response time | Mathematical analysis | Lasers | Integrals | Laser beam heating | Delay time | Vibration control | Phase lag | Numerical prediction | Graphical representations | Energy absorption | Laser beam hardening

Non-Gaussian laser pulse | Laplace Transform | memory dependent derivative | Finite Fourier transform | three-phase-lag thermoelastic model | microscale beam | THERMOELASTICITY | STRAIN GRADIENT PLASTICITY | MECHANICS | THERMODYNAMICS | DYNAMICS | HALF-SPACE | HARDNESS | PLATE | Kernel functions | Three phase | Derivatives | Pulsed lasers | Workpieces | Time dependence | Response time | Mathematical analysis | Lasers | Integrals | Laser beam heating | Delay time | Vibration control | Phase lag | Numerical prediction | Graphical representations | Energy absorption | Laser beam hardening

Journal Article

Computer Physics Communications, ISSN 0010-4655, 11/2015, Volume 196, pp. 226 - 235

A Runge–Kutta type twelfth algebraic order two-step method with vanished phase-lag and its first, second, third, fourth, fifth and sixth derivatives are...

Derivative of the phase-lag | Multistep | Phase-lag | Initial or boundary value problems | Schrödinger equation | PREDICTOR-CORRECTOR METHOD | SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | IVPS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | INTEGRATION | SCATTERING | SYMMETRIC MULTISTEP METHODS | Algebra | Mathematical analysis | Scalars | Truncation errors | Mathematical models | Runge-Kutta method | Schroedinger equation | Derivatives

Derivative of the phase-lag | Multistep | Phase-lag | Initial or boundary value problems | Schrödinger equation | PREDICTOR-CORRECTOR METHOD | SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | NUMERICAL-SOLUTION | IVPS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | INTEGRATION | SCATTERING | SYMMETRIC MULTISTEP METHODS | Algebra | Mathematical analysis | Scalars | Truncation errors | Mathematical models | Runge-Kutta method | Schroedinger equation | Derivatives

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 8/2014, Volume 52, Issue 7, pp. 1895 - 1920

An explicit linear sixth algebraic order six-step method with vanished phase-lag and its first derivative is constructed in this paper. We will study the...

65L05 | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Oscillating solution | Initial value problems | Multistep | Derivatives of the phase-lag | Phase-lag | Symmetric | Math. Applications in Chemistry | Schrödinger equation | PREDICTOR-CORRECTOR METHOD | RUNGE-KUTTA METHODS | HIGH-ORDER | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | RADIAL SCHRODINGER-EQUATION | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | SYMMETRIC MULTISTEP METHODS | Analysis | Frequencies of oscillating systems

65L05 | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Oscillating solution | Initial value problems | Multistep | Derivatives of the phase-lag | Phase-lag | Symmetric | Math. Applications in Chemistry | Schrödinger equation | PREDICTOR-CORRECTOR METHOD | RUNGE-KUTTA METHODS | HIGH-ORDER | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | RADIAL SCHRODINGER-EQUATION | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | SYMMETRIC MULTISTEP METHODS | Analysis | Frequencies of oscillating systems

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2008, Volume 1048, Issue 1, pp. 1020 - 1025

In this paper we consider the fitting of the coefficients of a numerical method, not only due to the nullification of the phase-lag, but also to its...

Oscillating solution | Initial value problems | Multistep | Derivatives | Phase-lag | MATHEMATICAL SOLUTIONS | NUMERICAL ANALYSIS | ERRORS | WAVE EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CALCULATION METHODS | ALGEBRA | OSCILLATIONS

Oscillating solution | Initial value problems | Multistep | Derivatives | Phase-lag | MATHEMATICAL SOLUTIONS | NUMERICAL ANALYSIS | ERRORS | WAVE EQUATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CALCULATION METHODS | ALGEBRA | OSCILLATIONS

Conference Proceeding

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 213, Issue 1, pp. 153 - 162

In this paper we study the spatial behaviour of solutions for the three-phase-lag heat equation on a semi-infinite cylinder. The theory of three-phase-lag heat...

Fourth-order derivative with respect to time | Hyperbolic partial differential equation | Spatial evolution on a semi-infinite cylinder | Three-phase-lag heat equation | MATHEMATICS, APPLIED | DECAY | THERMOELASTIC THEORY | STABILITY | CONDUCTION | PRINCIPLE | QUALITATIVE ASPECTS | Conducció | Anàlisi numèrica | Heat equation | Applied mathematics | Calor, Equació de | Matemàtiques i estadística | Calor | Àrees temàtiques de la UPC | Matemàtica aplicada

Fourth-order derivative with respect to time | Hyperbolic partial differential equation | Spatial evolution on a semi-infinite cylinder | Three-phase-lag heat equation | MATHEMATICS, APPLIED | DECAY | THERMOELASTIC THEORY | STABILITY | CONDUCTION | PRINCIPLE | QUALITATIVE ASPECTS | Conducció | Anàlisi numèrica | Heat equation | Applied mathematics | Calor, Equació de | Matemàtiques i estadística | Calor | Àrees temàtiques de la UPC | Matemàtica aplicada

Journal Article

Journal of Thermal Stresses, ISSN 0149-5739, 07/2019, Volume 42, Issue 7, pp. 874 - 889

The present study deals with the thermoelastic interaction in a semi-infinite elastic solid with a heat source in the context of three-phase-lag model with...

Laplace transform | memory-dependent derivative | three-phase-lag model | vector-matrix differential equation | Generalized thermoelasticity | MECHANICS | THERMODYNAMICS

Laplace transform | memory-dependent derivative | three-phase-lag model | vector-matrix differential equation | Generalized thermoelasticity | MECHANICS | THERMODYNAMICS

Journal Article

Mechanics of Advanced Materials and Structures, ISSN 1537-6494, 09/2013, Volume 20, Issue 8, pp. 593 - 602

In this work, a new mathematical model of heat conduction for an isotropic generalized thermoelasticity with a three-phase lag is derived using the methodology...

numerical results | three-phase lag | periodically varying heat sources | modified Riemann-Liouville fractional derivative | thermoelasticity | new fractional Taylor's series | Fourier law | GENERALIZED THERMO-VISCOELASTICITY | MATERIALS SCIENCE, MULTIDISCIPLINARY | RELAXATION | MATERIALS SCIENCE, COMPOSITES | ORDER THEORY | MODEL | modified RiemannLiouville fractional derivative | UNIQUENESS | MECHANICS | THEOREMS | MATERIALS SCIENCE, CHARACTERIZATION & TESTING | ENERGY-DISSIPATION | HEAT-CONDUCTION | Heat conduction | Conduction | Heat sources | Mathematical analysis | Thermoelasticity | Mathematical models | Calculus | Order parameters

numerical results | three-phase lag | periodically varying heat sources | modified Riemann-Liouville fractional derivative | thermoelasticity | new fractional Taylor's series | Fourier law | GENERALIZED THERMO-VISCOELASTICITY | MATERIALS SCIENCE, MULTIDISCIPLINARY | RELAXATION | MATERIALS SCIENCE, COMPOSITES | ORDER THEORY | MODEL | modified RiemannLiouville fractional derivative | UNIQUENESS | MECHANICS | THEOREMS | MATERIALS SCIENCE, CHARACTERIZATION & TESTING | ENERGY-DISSIPATION | HEAT-CONDUCTION | Heat conduction | Conduction | Heat sources | Mathematical analysis | Thermoelasticity | Mathematical models | Calculus | Order parameters

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 07/2018, Volume 1978, Issue 1

In this work we consider Two Derivative Runge-Kutta methods. We construct methods with constant coefficients and special properties as minimum phase-lag and...

phase lag | amplification error | Two Derivative Runge Kutta methods | Amplification | Runge-Kutta method | Phase lag

phase lag | amplification error | Two Derivative Runge Kutta methods | Amplification | Runge-Kutta method | Phase lag

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 11/2011, Volume 49, Issue 10, pp. 2486 - 2518

In this paper we introduce a new explicit hybrid Numerov-type method. This method is of fourth algebraic order and has phase-lag and its first two derivatives...

Phase-fitted | Schrödinger equation | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Hybrid methods | P-stability | Physical Chemistry | Numerical solution | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | HYBRID EXPLICIT METHODS | FITTING BDF ALGORITHMS | RUNGE-KUTTA METHODS | NUMEROV-TYPE METHODS | LONG-TIME INTEGRATION | ALGEBRAIC ORDER METHODS | CHEMISTRY, MULTIDISCIPLINARY | TRIGONOMETRICALLY-FITTED FORMULAS | PREDICTOR-CORRECTOR METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | SYMMETRIC MULTISTEP METHODS | SPECIAL-ISSUE | Numerical analysis | Research

Phase-fitted | Schrödinger equation | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Hybrid methods | P-stability | Physical Chemistry | Numerical solution | Multistep methods | Derivatives of the phase-lag | Phase-lag | Math. Applications in Chemistry | HYBRID EXPLICIT METHODS | FITTING BDF ALGORITHMS | RUNGE-KUTTA METHODS | NUMEROV-TYPE METHODS | LONG-TIME INTEGRATION | ALGEBRAIC ORDER METHODS | CHEMISTRY, MULTIDISCIPLINARY | TRIGONOMETRICALLY-FITTED FORMULAS | PREDICTOR-CORRECTOR METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | SYMMETRIC MULTISTEP METHODS | SPECIAL-ISSUE | Numerical analysis | Research

Journal Article