Applied Mathematics and Information Sciences, ISSN 1935-0090, 2013, Volume 7, Issue 2, pp. 433 - 437

In this paper, a new modified Runge-Kutta-Nystrom method of third algebraic order is developed. The new modified RKN method has phase-lag and amplification...

Oscillating solution | Initial value problems | Derivatives | Phase-fitted'8Amplification-fitted | Orbital problems | Runge-kutta-nyström methods | 2ND-ORDER IVPS | MATHEMATICS, APPLIED | initial value problems | oscillating solution | PHYSICS, MATHEMATICAL | Phase-fitted | RADIAL SCHRODINGER-EQUATION | Runge-Kutta-Nystrom methods | derivatives | TRIGONOMETRICALLY-FITTED METHODS | ORDER | Amplification-fitted | OSCILLATING SOLUTIONS

Oscillating solution | Initial value problems | Derivatives | Phase-fitted'8Amplification-fitted | Orbital problems | Runge-kutta-nyström methods | 2ND-ORDER IVPS | MATHEMATICS, APPLIED | initial value problems | oscillating solution | PHYSICS, MATHEMATICAL | Phase-fitted | RADIAL SCHRODINGER-EQUATION | Runge-Kutta-Nystrom methods | derivatives | TRIGONOMETRICALLY-FITTED METHODS | ORDER | Amplification-fitted | OSCILLATING SOLUTIONS

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 3/2014, Volume 52, Issue 3, pp. 917 - 947

The investigation of the impact of the vanishing of the phase-lag and its first and second derivatives on the efficiency of a four-step Runge–Kutta type method...

65L05 | Phase-fitted | Schrödinger equation | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Hybrid methods | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Runge–Kutta type methods | Phase-lag | Math. Applications in Chemistry | Runge-Kutta type methods | PREDICTOR-CORRECTOR METHOD | HYBRID EXPLICIT METHODS | SYMPLECTIC METHODS | HIGH-ORDER | INTERNATIONAL-CONFERENCE | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

65L05 | Phase-fitted | Schrödinger equation | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Hybrid methods | P-stability | Physical Chemistry | Multistep methods | Derivatives of the phase-lag | Runge–Kutta type methods | Phase-lag | Math. Applications in Chemistry | Runge-Kutta type methods | PREDICTOR-CORRECTOR METHOD | HYBRID EXPLICIT METHODS | SYMPLECTIC METHODS | HIGH-ORDER | INTERNATIONAL-CONFERENCE | LONG-TIME INTEGRATION | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | TRIGONOMETRICALLY-FITTED FORMULAS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2/2015, Volume 53, Issue 2, pp. 685 - 717

A predictor–corrector explicit four-step method of sixth algebraic order is investigated in this paper. More specifically, we investigate the results of the...

65L05 | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Physical Chemistry | Predictor–corrector methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Predictor-corrector methods | 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 | MULTIDERIVATIVE METHODS | NYSTROM METHOD | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

65L05 | Theoretical and Computational Chemistry | Interval of periodicity | Chemistry | Physical Chemistry | Predictor–corrector methods | Derivatives of the phase-lag | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | Predictor-corrector methods | 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 | MULTIDERIVATIVE METHODS | NYSTROM METHOD | SYMMETRIC MULTISTEP METHODS | Numerical analysis | Research | Mathematical research

Journal Article

FILOMAT, ISSN 0354-5180, 2017, Volume 31, Issue 15, pp. 4999 - 5012

The development of a new five-stages symmetric two-step method of fourteenth algebraic order with vanished phase-lag and its first, second, third and fourth...

PREDICTOR-CORRECTOR METHOD | ORBITAL PROBLEMS | MATHEMATICS, APPLIED | interval of periodicity | INITIAL-VALUE-PROBLEMS | SYMMETRIC 2-STEP METHOD | multistep methods | phase-lag | Multistage methods | MATHEMATICS | TRIGONOMETRICALLY-FITTED METHODS | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | Schrodinger equation | derivatives of the phase-lag | KUTTA-NYSTROM METHODS | phase-fitted | P-STABLE METHOD

PREDICTOR-CORRECTOR METHOD | ORBITAL PROBLEMS | MATHEMATICS, APPLIED | interval of periodicity | INITIAL-VALUE-PROBLEMS | SYMMETRIC 2-STEP METHOD | multistep methods | phase-lag | Multistage methods | MATHEMATICS | TRIGONOMETRICALLY-FITTED METHODS | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | Schrodinger equation | derivatives of the phase-lag | KUTTA-NYSTROM METHODS | phase-fitted | P-STABLE METHOD

Journal Article

Measurement, ISSN 0263-2241, 10/2016, Volume 92, pp. 83 - 88

•Self-developed signal processing method is proposed.•By spectrum analysis, the sub-frequency can be observed.•The sub-frequency can be significantly minimized...

Fabry–Perot interferometer | Frequency spectrum | Lookup table (LUT) method | Fitted method | Interpolation model | Fabry-Perot interferometer | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | SENSOR | Measurement | Signal processing | Optical instruments | Analysis | Methods | Mechanical engineering

Fabry–Perot interferometer | Frequency spectrum | Lookup table (LUT) method | Fitted method | Interpolation model | Fabry-Perot interferometer | INSTRUMENTS & INSTRUMENTATION | ENGINEERING, MULTIDISCIPLINARY | SENSOR | Measurement | Signal processing | Optical instruments | Analysis | Methods | Mechanical engineering

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

Numerical Algorithms, ISSN 1017-1398, 1/2013, Volume 62, Issue 1, pp. 13 - 26

A trigonometrically fitted block Numerov type method (TBNM), is proposed for solving y′′ = f(x, y, y′) directly without reducing it to an equivalent first...

Second order | Algorithms | Algebra | Trigonometrically fitted method | Block form | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Initial value problems | Construction | Numerical analysis | Stability | Equivalence | Blocking | Mathematical models | Integrators | Representations

Second order | Algorithms | Algebra | Trigonometrically fitted method | Block form | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Initial value problems | Construction | Numerical analysis | Stability | Equivalence | Blocking | Mathematical models | Integrators | Representations

Journal Article

Computer Physics Communications, ISSN 0010-4655, 2009, Volume 180, Issue 10, pp. 1839 - 1846

A new Runge–Kutta–Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this...

Runge–Kutta–Nyström methods | Phase-lag infinity | Phase-fitted | Initial-value problems | Runge-Kutta-Nyström methods | Runge-Kutta-Nystrom methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LAG | INTEGRATION | SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | NOUMEROV-TYPE METHOD

Runge–Kutta–Nyström methods | Phase-lag infinity | Phase-fitted | Initial-value problems | Runge-Kutta-Nyström methods | Runge-Kutta-Nystrom methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LAG | INTEGRATION | SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | NOUMEROV-TYPE METHOD

Journal Article

Applied Mathematics and Information Sciences, ISSN 1935-0090, 01/2013, Volume 7, Issue 1, pp. 73 - 80

In this paper we present a new optimized symmetric eight-step semi-embedded predictor-corrector method (SEPCM) with minimal phase-lag. The method is based on...

Orbital problems | Predictor-corrector | Semiembedded | Oscillating solution | Multistep | Symmetric | Phase-lag, initial value problems | 2ND-ORDER IVPS | MATHEMATICS, APPLIED | initial value problems | phase-lag | oscillating solution | predictor-corrector | PHYSICS, MATHEMATICAL | symmetric | RADIAL SCHRODINGER-EQUATION | TRIGONOMETRICALLY-FITTED METHODS | ORDER | NUMERICAL-SOLUTION | MULTISTEP METHODS | multistep | semi-embedded

Orbital problems | Predictor-corrector | Semiembedded | Oscillating solution | Multistep | Symmetric | Phase-lag, initial value problems | 2ND-ORDER IVPS | MATHEMATICS, APPLIED | initial value problems | phase-lag | oscillating solution | predictor-corrector | PHYSICS, MATHEMATICAL | symmetric | RADIAL SCHRODINGER-EQUATION | TRIGONOMETRICALLY-FITTED METHODS | ORDER | NUMERICAL-SOLUTION | MULTISTEP METHODS | multistep | semi-embedded

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

Journal of Applied Mathematics, ISSN 1110-757X, 4/2012, Volume 2012, pp. 1 - 17

We use a methodology of optimization of the efficiency of a hybrid two-step method for the numerical solution of the radial Schrödinger equation and related...

KUTTA-NYSTROM FORMULAS | TRIGONOMETRICALLY-FITTED METHODS | 2ND-ORDER IVPS | SCHEME | MATHEMATICS, APPLIED | MULTISTEP METHODS | INITIAL-VALUE-PROBLEMS | HIGH-ORDER | OSCILLATING SOLUTIONS | SYMPLECTIC INTEGRATORS | Studies | Problems | Accuracy | Algorithms | Algebra | Efficiency | Mathematical models | Methods | Methodology | Oscillating | Schroedinger equation | Computational efficiency | Derivatives | Computing time | Optimization

KUTTA-NYSTROM FORMULAS | TRIGONOMETRICALLY-FITTED METHODS | 2ND-ORDER IVPS | SCHEME | MATHEMATICS, APPLIED | MULTISTEP METHODS | INITIAL-VALUE-PROBLEMS | HIGH-ORDER | OSCILLATING SOLUTIONS | SYMPLECTIC INTEGRATORS | Studies | Problems | Accuracy | Algorithms | Algebra | Efficiency | Mathematical models | Methods | Methodology | Oscillating | Schroedinger equation | Computational efficiency | Derivatives | Computing time | Optimization

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

Advances in Mathematical Physics, ISSN 1687-9120, 11/2016, Volume 2016, pp. 1 - 20

The development of a new five-stage symmetric two-step fourteenth-algebraic order method with vanished phase-lag and its first, second, and third derivatives...

TRIGONOMETRICALLY-FITTED METHODS | PREDICTOR-CORRECTOR METHOD | VANISHED PHASE-LAG | 4TH DERIVATIVES | MULTISTEP METHODS | SYMMETRIC 2-STEP METHOD | KUTTA-NYSTROM METHOD | HIGH-ORDER | P-STABLE METHOD | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | Boundary conditions | Informatics | Methods | Physics

TRIGONOMETRICALLY-FITTED METHODS | PREDICTOR-CORRECTOR METHOD | VANISHED PHASE-LAG | 4TH DERIVATIVES | MULTISTEP METHODS | SYMMETRIC 2-STEP METHOD | KUTTA-NYSTROM METHOD | HIGH-ORDER | P-STABLE METHOD | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | Boundary conditions | Informatics | Methods | Physics

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 2/2010, Volume 47, Issue 2, pp. 871 - 890

With this paper, a new algorithm is developed for the numerical solution of the one-dimensional Schrödinger equation. The new method uses the minimum order of...

Theoretical and Computational Chemistry | Chemistry | Hybrid methods | Physical Chemistry | Multistep methods | Explicit methods | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | RUNGE-KUTTA METHODS | EXPONENTIAL-FITTING METHODS | FINITE-DIFFERENCE METHOD | ALGEBRAIC ORDER METHODS | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | PREDICTOR-CORRECTOR METHODS | TRIGONOMETRICALLY-FITTED FORMULAS | MINIMAL PHASE-LAG | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | SYMMETRIC MULTISTEP METHODS | Usage | Algorithms | Analysis

Theoretical and Computational Chemistry | Chemistry | Hybrid methods | Physical Chemistry | Multistep methods | Explicit methods | Phase-lag | Phase-fitted | Math. Applications in Chemistry | Schrödinger equation | RUNGE-KUTTA METHODS | EXPONENTIAL-FITTING METHODS | FINITE-DIFFERENCE METHOD | ALGEBRAIC ORDER METHODS | CHEMISTRY, MULTIDISCIPLINARY | INITIAL-VALUE PROBLEMS | PREDICTOR-CORRECTOR METHODS | TRIGONOMETRICALLY-FITTED FORMULAS | MINIMAL PHASE-LAG | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | NUMEROV-TYPE METHOD | SYMMETRIC MULTISTEP METHODS | Usage | Algorithms | Analysis

Journal Article

Journal of Computational Chemistry, ISSN 0192-8651, 10/2014, Volume 35, Issue 28, pp. 2019 - 2026

The performance of 18 density functional approximations has been tested for a very challenging task, the calculations of rate constants for radical‐molecule...

long‐range correction | rate constants | dispersion | density functional theory | exact exchange | empirically fitted parameters | Long-range correction | Density functional theory | Rate constants | Empirically fitted parameters | Exact exchange | Dispersion | long-range correction | CONSTRAINT SATISFACTION | THERMOCHEMICAL KINETICS | ELECTRON-TRANSFER-REACTIONS | NONCOVALENT INTERACTIONS | CHEMISTRY, MULTIDISCIPLINARY | HYDROXYL RADICALS | PULSE-RADIOLYSIS | HYDROGEN-ATOMS | BARRIER HEIGHTS | PROTON-TRANSFER

long‐range correction | rate constants | dispersion | density functional theory | exact exchange | empirically fitted parameters | Long-range correction | Density functional theory | Rate constants | Empirically fitted parameters | Exact exchange | Dispersion | long-range correction | CONSTRAINT SATISFACTION | THERMOCHEMICAL KINETICS | ELECTRON-TRANSFER-REACTIONS | NONCOVALENT INTERACTIONS | CHEMISTRY, MULTIDISCIPLINARY | HYDROXYL RADICALS | PULSE-RADIOLYSIS | HYDROGEN-ATOMS | BARRIER HEIGHTS | PROTON-TRANSFER

Journal Article