Journal of Mathematical Chemistry, ISSN 0259-9791, 5/2019, Volume 57, Issue 5, pp. 1413 - 1426

A new embedded 4(3) pair of modified two-derivative Runge–Kutta (TDRK) methods with First Same As Last (FSAL) property for the numerical solution of the...

Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Embedded TDRK pair | Math. Applications in Chemistry | Lennard-Jones potential | Schrödinger equation | FOURIER COLLOCATION METHODS | ALGORITHMS | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | MINIMAL PHASE-LAG | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | MULTISTEP METHODS | INTEGRATION | NUMEROV | HIGH-ORDER METHOD | 4-STEP METHOD | EXPLICIT | Numerical analysis | Research | Mathematical research

Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Embedded TDRK pair | Math. Applications in Chemistry | Lennard-Jones potential | Schrödinger equation | FOURIER COLLOCATION METHODS | ALGORITHMS | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | MINIMAL PHASE-LAG | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | MULTISTEP METHODS | INTEGRATION | NUMEROV | HIGH-ORDER METHOD | 4-STEP METHOD | EXPLICIT | Numerical analysis | Research | Mathematical research

Journal Article

PLoS ONE, ISSN 1932-6203, 09/2013, Volume 8, Issue 9, p. e76354

Background: Benefits of skills lab training are widely accepted, but there is sparse research on its long-term effectiveness. We therefore conducted a...

4-STEP APPROACH | DELIBERATE PRACTICE | INTEGRATION | RETENTION | MULTIDISCIPLINARY SCIENCES | STANDARDIZED PATIENTS | ACQUISITION | COMPETENCE | SIMULATION | INTERVENTION | CARE | Clinical Competence | Clinical Laboratory Techniques - methods | Intubation, Gastrointestinal - methods | Catheterization - methods | Statistics, Nonparametric | Education, Medical, Undergraduate - methods | Teaching - methods | Practice Guidelines as Topic | Medical students | Training | Medical personnel | Education | Learning strategies | College students | Universities and colleges | Methods | Nephrology | Intravenous administration | Psychotherapy | Retention | Complexity | Learning | Students | Skills | Feedback | Colonoscopy | Check lists | Computer simulation | Independent study | Curricula | Cannulation | Laparoscopy | Health education | Psychosomatic medicine | Medicine | Studies | Teaching methods | Hospitals | Simulation | Diabetes | Endocrinology | Best practice

4-STEP APPROACH | DELIBERATE PRACTICE | INTEGRATION | RETENTION | MULTIDISCIPLINARY SCIENCES | STANDARDIZED PATIENTS | ACQUISITION | COMPETENCE | SIMULATION | INTERVENTION | CARE | Clinical Competence | Clinical Laboratory Techniques - methods | Intubation, Gastrointestinal - methods | Catheterization - methods | Statistics, Nonparametric | Education, Medical, Undergraduate - methods | Teaching - methods | Practice Guidelines as Topic | Medical students | Training | Medical personnel | Education | Learning strategies | College students | Universities and colleges | Methods | Nephrology | Intravenous administration | Psychotherapy | Retention | Complexity | Learning | Students | Skills | Feedback | Colonoscopy | Check lists | Computer simulation | Independent study | Curricula | Cannulation | Laparoscopy | Health education | Psychosomatic medicine | Medicine | Studies | Teaching methods | Hospitals | Simulation | Diabetes | Endocrinology | Best practice

Journal Article

Match, ISSN 0340-6253, 2015, Volume 73, Issue 3, pp. 619 - 648

A new two-step high algebraic order (tenth order) two-step hybrid (Runge-Kutta type) method is developed in this paper. For this new method we require the...

PREDICTOR-CORRECTOR METHOD | KUTTA-NYSTROM METHOD | SCHRODINGER-EQUATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | SYMMETRIC METHODS | TRIGONOMETRICALLY-FITTED METHODS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTISTEP METHODS | EFFICIENT INTEGRATION | 4-STEP METHODS

PREDICTOR-CORRECTOR METHOD | KUTTA-NYSTROM METHOD | SCHRODINGER-EQUATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | SYMMETRIC METHODS | TRIGONOMETRICALLY-FITTED METHODS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTISTEP METHODS | EFFICIENT INTEGRATION | 4-STEP METHODS

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2/2016, Volume 54, Issue 2, pp. 442 - 465

A two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives with low computational cost is developed in...

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | 2ND-ORDER IVPS | KUTTA-NYSTROM METHOD | HIGH-ORDER | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | MULTISTEP METHODS | EFFICIENT INTEGRATION | EXPLICIT 4-STEP METHOD | SYMPLECTIC INTEGRATORS | Analysis

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | 2ND-ORDER IVPS | KUTTA-NYSTROM METHOD | HIGH-ORDER | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | MULTISTEP METHODS | EFFICIENT INTEGRATION | EXPLICIT 4-STEP METHOD | SYMPLECTIC INTEGRATORS | Analysis

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 4/2017, Volume 55, Issue 4, pp. 987 - 1013

A computationally economical symmetric six-step algorithm with high algebraic and phase-lag order is obtained in this paper, for the first time in the...

65L05 | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Multistage methods | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | OPTIMIZED GENERATOR | EFFICIENT INTEGRATION | KUTTA-NYSTROM METHODS | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

65L05 | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Multistage methods | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | OPTIMIZED GENERATOR | EFFICIENT INTEGRATION | KUTTA-NYSTROM METHODS | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 1/2017, Volume 55, Issue 1, pp. 105 - 131

The presentation, development and analysis of a new two-stages tenth algebraic order symmetric six-step method is introduced, for the first time in the...

65L05 | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Multistage methods | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Analysis | Symmetry groups

65L05 | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Multistage methods | PREDICTOR-CORRECTOR METHOD | SYMPLECTIC METHODS | RUNGE-KUTTA METHODS | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Analysis | Symmetry groups

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 1/2018, Volume 56, Issue 1, pp. 170 - 192

A new finite difference pair is produced in this paper, for the first time in the literature. The characteristics of the new finite diffence pair are: (1) is...

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | SYMMETRIC 2-STEP METHOD | KUTTA-NYSTROM METHOD | SCHRODINGER-EQUATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Finite element method | Research | Mathematical research

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | SYMMETRIC 2-STEP METHOD | KUTTA-NYSTROM METHOD | SCHRODINGER-EQUATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Finite element method | Research | Mathematical research

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2/2017, Volume 55, Issue 2, pp. 503 - 531

In the present paper, we obtain and analyze, for the first time in the literature, a new two-stages high order symmetric six-step method. The specific...

Theoretical and Computational Chemistry | Interval of periodicity | Derivatives of the phase–lag | Chemistry | Physical Chemistry | Multistep methods | Phase–lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Multistage methods | 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 | Derivatives of the phase-lag | Phase-lag | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Usage | Quantum chemistry | Analysis

Theoretical and Computational Chemistry | Interval of periodicity | Derivatives of the phase–lag | Chemistry | Physical Chemistry | Multistep methods | Phase–lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Multistage methods | 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 | Derivatives of the phase-lag | Phase-lag | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Usage | Quantum chemistry | Analysis

Journal Article

9.
Full Text
Explicit hybrid six–step, sixth order, fully symmetric methods for solving y ″ = f (x,y)

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 06/2019, Volume 42, Issue 9, pp. 3305 - 3314

A family of explicit, fully symmetric, sixth order, six‐step methods for the numerical solution of y′′ = f(x,y) is studied. This family wastes two function...

multistep | phase lag | constant coefficients | initial value problem | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | NUMEROV-TYPE METHODS | SCHRODINGER-EQUATION | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | FITTED MODIFICATIONS | EFFICIENT INTEGRATION | RUNGE-KUTTA PAIRS | P-STABLE METHOD | 4-STEP METHODS | Interpolation | Phase lag | Periodic variations | Numerical methods

multistep | phase lag | constant coefficients | initial value problem | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | NUMEROV-TYPE METHODS | SCHRODINGER-EQUATION | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | FITTED MODIFICATIONS | EFFICIENT INTEGRATION | RUNGE-KUTTA PAIRS | P-STABLE METHOD | 4-STEP METHODS | Interpolation | Phase lag | Periodic variations | Numerical methods

Journal Article

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, ISSN 0340-6253, 2017, Volume 77, Issue 2, pp. 333 - 392

In this paper we obtain, for the first time in the literature, a new twelfth algebraic order four stages symmetric two step method. The method is produced,...

PREDICTOR-CORRECTOR METHOD | INITIAL-VALUE-PROBLEMS | KUTTA-NYSTROM METHOD | CHEMISTRY, MULTIDISCIPLINARY | SYMMETRIC METHODS | TRIGONOMETRICALLY-FITTED METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTISTEP METHODS | EFFICIENT INTEGRATION | P-STABLE METHOD | 4-STEP METHODS | OSCILLATING SOLUTIONS

PREDICTOR-CORRECTOR METHOD | INITIAL-VALUE-PROBLEMS | KUTTA-NYSTROM METHOD | CHEMISTRY, MULTIDISCIPLINARY | SYMMETRIC METHODS | TRIGONOMETRICALLY-FITTED METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTISTEP METHODS | EFFICIENT INTEGRATION | P-STABLE METHOD | 4-STEP METHODS | OSCILLATING SOLUTIONS

Journal Article

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, ISSN 0340-6253, 2017, Volume 77, Issue 2, pp. 527 - 568

A new high algebraic order four stages symmetric two step method is developed, for the first time in the literature, in the present paper. Requesting the...

PREDICTOR-CORRECTOR METHOD | INITIAL-VALUE-PROBLEMS | KUTTA-NYSTROM METHOD | CHEMISTRY, MULTIDISCIPLINARY | SYMMETRIC METHODS | TRIGONOMETRICALLY-FITTED METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTISTEP METHODS | EFFICIENT INTEGRATION | P-STABLE METHOD | 4-STEP METHODS | OSCILLATING SOLUTIONS

PREDICTOR-CORRECTOR METHOD | INITIAL-VALUE-PROBLEMS | KUTTA-NYSTROM METHOD | CHEMISTRY, MULTIDISCIPLINARY | SYMMETRIC METHODS | TRIGONOMETRICALLY-FITTED METHODS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTISTEP METHODS | EFFICIENT INTEGRATION | P-STABLE METHOD | 4-STEP METHODS | OSCILLATING SOLUTIONS

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 1/2019, Volume 57, Issue 1, pp. 232 - 262

A new multiple stages two–step scheme with best possible properties on phase and stability is introduced, for the first time in the literature. For this scheme...

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | SYMMETRIC 2-STEP METHOD | KUTTA-NYSTROM METHOD | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED METHODS | VANISHED PHASE-LAG | FINITE-DIFFERENCE PAIR | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | EXPLICIT 4-STEP METHODS | P-STABLE METHOD

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | SYMMETRIC 2-STEP METHOD | KUTTA-NYSTROM METHOD | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED METHODS | VANISHED PHASE-LAG | FINITE-DIFFERENCE PAIR | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | EXPLICIT 4-STEP METHODS | P-STABLE METHOD

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2/2018, Volume 56, Issue 2, pp. 449 - 476

In this paper and for the first time in the literature, a new four-stages symmetric two-step finite difference pair with optimized phase and stability...

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | INITIAL-VALUE-PROBLEMS | SYMMETRIC 2-STEP METHOD | CHEMISTRY, MULTIDISCIPLINARY | RADIAL SCHRODINGER-EQUATION | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | KUTTA-NYSTROM METHODS | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Approximation theory | Numerical analysis | Research | Mathematical research

65L05 | Hybrid | Oscillating solution | Multistep | Schrödinger equation | Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Derivative of the phase-lag | Initial value problems | Phase-lag | Symmetric | Math. Applications in Chemistry | PREDICTOR-CORRECTOR METHOD | NUMEROV-TYPE METHODS | INITIAL-VALUE-PROBLEMS | SYMMETRIC 2-STEP METHOD | CHEMISTRY, MULTIDISCIPLINARY | RADIAL SCHRODINGER-EQUATION | TRIGONOMETRICALLY-FITTED FORMULAS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | KUTTA-NYSTROM METHODS | P-STABLE METHOD | EXPLICIT 4-STEP METHOD | Approximation theory | Numerical analysis | Research | Mathematical research

Journal Article