Journal of Computational Physics, ISSN 0021-9991, 02/2014, Volume 259, pp. 33 - 50

In the present work, first, a new fractional numerical differentiation formula (called the L1-2 formula) to approximate the Caputo fractional derivative of...

L1 formula | Sub-diffusion | Fractional numerical differentiation formula | Caputo fractional derivative | L1-2 formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SUB-DIFFUSION EQUATIONS | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE SCHEME | Interpolation | Accuracy | Approximation | Mathematical analysis | Differential equations | Mathematical models | Derivatives | Finite difference method | Formulas (mathematics)

L1 formula | Sub-diffusion | Fractional numerical differentiation formula | Caputo fractional derivative | L1-2 formula | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SUB-DIFFUSION EQUATIONS | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE SCHEME | Interpolation | Accuracy | Approximation | Mathematical analysis | Differential equations | Mathematical models | Derivatives | Finite difference method | Formulas (mathematics)

Journal Article

Nuclear Engineering and Design, ISSN 0029-5493, 01/2019, Volume 341, pp. 220 - 238

•This paper discusses the generation of depletion of radioisotopes in the nuclear reactor.•This is basically the problem of solving nonlinear Bateman...

NUCLEAR SCIENCE & TECHNOLOGY | NUCLEAR | Nuclear energy | Usage | Heavy water | Uranium | Nuclear reactors | Nuclear facilities | Deuterium | Heavy water reactors | Toxicity | Pressure distribution | Nuclear engineering | Pressure | Fuel cycles | Fission products | Actinides | Nuclear fuels | Depletion | Reactors | Differential equations | Nuclear reactor components | Isotopes | Nuclear fission | Numerical differentiation | Radioactivity

NUCLEAR SCIENCE & TECHNOLOGY | NUCLEAR | Nuclear energy | Usage | Heavy water | Uranium | Nuclear reactors | Nuclear facilities | Deuterium | Heavy water reactors | Toxicity | Pressure distribution | Nuclear engineering | Pressure | Fuel cycles | Fission products | Actinides | Nuclear fuels | Depletion | Reactors | Differential equations | Nuclear reactor components | Isotopes | Nuclear fission | Numerical differentiation | Radioactivity

Journal Article

Journal of the Franklin Institute, ISSN 0016-0032, 03/2019, Volume 356, Issue 4, pp. 2130 - 2152

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated....

DESIGN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | STABILITY ANALYSIS | PURE-FEEDBACK SYSTEMS | FINITE-TIME CONVERGENCE | ZHANG NEURAL-NETWORK | ADAPTIVE-CONTROL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Information science | Neural networks | Artificial intelligence | Analysis | Mathematical problems | Numerical analysis | Discretization | Integral equations | Integrals | Discrete time systems | Error functions | Mathematical models | Discrete element method | Formulas (mathematics) | Numerical differentiation

DESIGN | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | STABILITY ANALYSIS | PURE-FEEDBACK SYSTEMS | FINITE-TIME CONVERGENCE | ZHANG NEURAL-NETWORK | ADAPTIVE-CONTROL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Information science | Neural networks | Artificial intelligence | Analysis | Mathematical problems | Numerical analysis | Discretization | Integral equations | Integrals | Discrete time systems | Error functions | Mathematical models | Discrete element method | Formulas (mathematics) | Numerical differentiation

Journal Article

Journal of Mathematical Sciences (United States), ISSN 1072-3374, 11/2018, Volume 235, Issue 2, pp. 138 - 153

We consider an approximation method based on Steklov functions of the first and second order. We obtain estimates for the norms in the space C of continuous...

NUMERICAL ANALYSIS | FUNCTIONS | APPROXIMATIONS | DIFFERENTIAL CALCULUS | PERIODICITY | MATHEMATICAL METHODS AND COMPUTING

NUMERICAL ANALYSIS | FUNCTIONS | APPROXIMATIONS | DIFFERENTIAL CALCULUS | PERIODICITY | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 10/2018, Volume 41, Issue 4, pp. 2053 - 2066

We write expressions connected with numerical differentiation formulas of order 2 in the form of Stieltjes integral, then we use Ohlin lemma and Levin–Stechkin...

39B62 | 26A51 | Differentiation formulas | 26D10 | Mathematics, general | Mathematics | Hermite–Hadamard inequality | Convex functions | Applications of Mathematics | MATHEMATICS | Hermite-Hadamard inequality | Stieltjes integral | Numerical differentiation | Inequalities

39B62 | 26A51 | Differentiation formulas | 26D10 | Mathematics, general | Mathematics | Hermite–Hadamard inequality | Convex functions | Applications of Mathematics | MATHEMATICS | Hermite-Hadamard inequality | Stieltjes integral | Numerical differentiation | Inequalities

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2005, Volume 183, Issue 1, pp. 29 - 52

Through introducing the generalized Vandermonde determinant, the linear algebraic system of a kind of Vandermonde equations is solved analytically by use of...

Higher derivatives | Taylor series | Explicit finite difference formula | Numerical differentiation | Generalized Vandermonde determinant | MATHEMATICS, APPLIED | APPROXIMATIONS | explicit finite difference formula | numerical differentiation | EXPRESSIONS | higher derivatives | TAYLOR-SERIES | MATHEMATICAL PROOF | REGULARIZATION | DERIVATIVES | DIGITAL DIFFERENTIATORS | generalized Vandermonde determinant | Atmospheric physics | Algorithms | Fluid dynamics | Analysis

Higher derivatives | Taylor series | Explicit finite difference formula | Numerical differentiation | Generalized Vandermonde determinant | MATHEMATICS, APPLIED | APPROXIMATIONS | explicit finite difference formula | numerical differentiation | EXPRESSIONS | higher derivatives | TAYLOR-SERIES | MATHEMATICAL PROOF | REGULARIZATION | DERIVATIVES | DIGITAL DIFFERENTIATORS | generalized Vandermonde determinant | Atmospheric physics | Algorithms | Fluid dynamics | Analysis

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2013, Volume 239, Issue 1, pp. 406 - 414

In order to achieve higher computational precision in approximating the first-order derivative of the target point, the 1-step-ahead numerical differentiation...

1-step-ahead | Error analysis | The first-order derivative | Computational precision | Optimal step length | Numerical differentiation | EXPRESSIONS | MATHEMATICS, APPLIED | RECURRENT NEURAL-NETWORK | TAYLOR-SERIES | FINITE-DIFFERENCE APPROXIMATIONS | Approximation | Computation | Mathematical analysis | Mathematical models | Derivatives | Optimization

1-step-ahead | Error analysis | The first-order derivative | Computational precision | Optimal step length | Numerical differentiation | EXPRESSIONS | MATHEMATICS, APPLIED | RECURRENT NEURAL-NETWORK | TAYLOR-SERIES | FINITE-DIFFERENCE APPROXIMATIONS | Approximation | Computation | Mathematical analysis | Mathematical models | Derivatives | Optimization

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2009, Volume 160, Issue 1, pp. 202 - 222

First, we briefly discuss three classes of numerical differentiation formulae, namely finite difference methods, the method of contour integration, and...

Error bounds | Entire functions of exponential type | Sampling method | Numerical differentiation | Gaussian multiplier | INTERPOLATION | POLYNOMIALS | MATHEMATICS | ANALYTIC FUNCTIONS | CONVERGENCE

Error bounds | Entire functions of exponential type | Sampling method | Numerical differentiation | Gaussian multiplier | INTERPOLATION | POLYNOMIALS | MATHEMATICS | ANALYTIC FUNCTIONS | CONVERGENCE

Journal Article

IEEE Transactions on Geoscience and Remote Sensing, ISSN 0196-2892, 06/2014, Volume 52, Issue 6, pp. 3513 - 3528

The K distribution can arguably be regarded as one of the most successful and widely used models for radar data. However, in the last two decades, we have seen...

Shape | Mellin-kind statistics (MKS) | Estimation | Speckle | generalized inverse Gaussian (GIG) | Covariance matrices | Kummer- {\cal U} distribution | numerical differentiation | radar statistics | synthetic aperture radar (SAR) | Fisher | method of log cumulants (MoLC) | polarimetric {\cal G} distribution | Data models | Random variables | Synthetic aperture radar | Gaussian distribution | Usage | Kernel functions | Mathematical statistics | Innovations | Parameter estimation | Radar

Shape | Mellin-kind statistics (MKS) | Estimation | Speckle | generalized inverse Gaussian (GIG) | Covariance matrices | Kummer- {\cal U} distribution | numerical differentiation | radar statistics | synthetic aperture radar (SAR) | Fisher | method of log cumulants (MoLC) | polarimetric {\cal G} distribution | Data models | Random variables | Synthetic aperture radar | Gaussian distribution | Usage | Kernel functions | Mathematical statistics | Innovations | Parameter estimation | Radar

Journal Article

IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 11/2018, Volume 29, Issue 11, pp. 5767 - 5776

In this brief, a new one-step-ahead numerical differentiation rule called six-instant g...

new-type discrete-time Zhang neural network (DTZNN) models | Analytical models | Dynamic linear equation system | Heuristic algorithms | Computational modeling | time-varying rank-deficient coefficient | Numerical models | Mathematical model | Integrated circuit modeling | Time-varying systems | least-squares solution | g -cube finite difference (6Ig CFD) formula">six-instant g -cube finite difference (6Ig CFD) formula | six-instant g-cube finite difference (6IgCFD) formula | OPTIMIZATION PROBLEMS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | MATRIX-INVERSION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | RECURRENT NEURAL-NETWORK | ROBUSTNESS ANALYSIS | COMPUTER SCIENCE, THEORY & METHODS | HYBRID | Neural networks | Least squares method | Computer applications | Mathematical models | Linear equations | Coefficients | Formulas (mathematics) | Numerical differentiation | Finite difference method

new-type discrete-time Zhang neural network (DTZNN) models | Analytical models | Dynamic linear equation system | Heuristic algorithms | Computational modeling | time-varying rank-deficient coefficient | Numerical models | Mathematical model | Integrated circuit modeling | Time-varying systems | least-squares solution | g -cube finite difference (6I

Journal Article

Computer Physics Communications, ISSN 0010-4655, 2008, Volume 179, Issue 11, pp. 773 - 776

In an earlier article, we had indicated two applications where there was a significant improvement in accuracy due to the use of higher order approximation for...

Radioactivity migration in porous medium and MST formula | Method of undetermined coefficients | Numerical differentiation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MST formula | DISCRETE VARIABLE REPRESENTATION | RATE CONSTANTS | FLUX | PHYSICS, MATHEMATICAL | Radioactivity migration in porous medium

Radioactivity migration in porous medium and MST formula | Method of undetermined coefficients | Numerical differentiation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MST formula | DISCRETE VARIABLE REPRESENTATION | RATE CONSTANTS | FLUX | PHYSICS, MATHEMATICAL | Radioactivity migration in porous medium

Journal Article

Modeling and Analysis of Information Systems, ISSN 1818-1015, 06/2016, Volume 23, Issue 3, pp. 377 - 384

Interpolation of functions on the basis of Lagrange’s polynomials is widely used. However in the case when the function has areas of large gradients,...

boundary layer component | error estimate | quadrature formulas | nonpolynomial interpolation | formulas of numerical diﬀerentiation | function of one variable

boundary layer component | error estimate | quadrature formulas | nonpolynomial interpolation | formulas of numerical diﬀerentiation | function of one variable

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 231, Issue 2, pp. 907 - 913

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the...

Elementary symmetric function | Lagrange interpolation | Cycle indicator of symmetric group | Numerical differentiation | MATHEMATICS, APPLIED | INTERPOLATION | EXPRESSIONS | ORDER | TAYLOR-SERIES | MATHEMATICAL PROOF | DERIVATIVES | DIGITAL DIFFERENTIATORS | FINITE-DIFFERENCE APPROXIMATIONS

Elementary symmetric function | Lagrange interpolation | Cycle indicator of symmetric group | Numerical differentiation | MATHEMATICS, APPLIED | INTERPOLATION | EXPRESSIONS | ORDER | TAYLOR-SERIES | MATHEMATICAL PROOF | DERIVATIVES | DIGITAL DIFFERENTIATORS | FINITE-DIFFERENCE APPROXIMATIONS

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 230, Issue 2, pp. 418 - 423

Through exploiting the generalized Lagrange interpolation for continuous piecewise smooth functions, a remainder term of numerical differentiation is given....

Divided difference | Lagrange interpolation | Numerical differentiation | EXPRESSIONS | MATHEMATICS, APPLIED | TAYLOR-SERIES | MATHEMATICAL PROOF | DERIVATIVES | DIGITAL DIFFERENTIATORS | FINITE-DIFFERENCE APPROXIMATIONS

Divided difference | Lagrange interpolation | Numerical differentiation | EXPRESSIONS | MATHEMATICS, APPLIED | TAYLOR-SERIES | MATHEMATICAL PROOF | DERIVATIVES | DIGITAL DIFFERENTIATORS | FINITE-DIFFERENCE APPROXIMATIONS

Journal Article

15.
Full Text
On the instability of symmetric formulas for numerical differentiation and integration

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 6/2015, Volume 55, Issue 6, pp. 917 - 921

The stability of the order of symmetric formulas for derivative approximation used in finite-difference methods for solving differential equations is analyzed....

numerical differentiation | Computational Mathematics and Numerical Analysis | approximation of derivatives | rectangular quadrature formula | order of the remainder term | stability of the order of a formula | Mathematics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Studies | Numerical analysis | Mathematical analysis | Physics | Approximations | Stability | Approximation | Instability | Mathematical models | Derivatives | Quadratures | Symmetry

numerical differentiation | Computational Mathematics and Numerical Analysis | approximation of derivatives | rectangular quadrature formula | order of the remainder term | stability of the order of a formula | Mathematics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Studies | Numerical analysis | Mathematical analysis | Physics | Approximations | Stability | Approximation | Instability | Mathematical models | Derivatives | Quadratures | Symmetry

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 12/2017, Volume 73, Issue 2, pp. 617 - 643

In this paper we develop a parallel method for solving possibly non-convex time-dependent Hamilton–Jacobi equations arising from optimal control and...

Hopf–Lax formula | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Optimal control | Mathematical and Computational Engineering | Mathematics | Hamilton–Jacobi equations | Differential game | COORDINATE DESCENT METHOD | Hamilton-Jacobi equations | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | CONVERGENCE | OPTIMIZATION | Hopf-Lax formula | REACHABLE SETS | Usage

Hopf–Lax formula | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Optimal control | Mathematical and Computational Engineering | Mathematics | Hamilton–Jacobi equations | Differential game | COORDINATE DESCENT METHOD | Hamilton-Jacobi equations | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | CONVERGENCE | OPTIMIZATION | Hopf-Lax formula | REACHABLE SETS | Usage

Journal Article

Computer Physics Communications, ISSN 0010-4655, 2004, Volume 161, Issue 3, pp. 109 - 118

In many situations, the numerical derivative of a function at a point x must be calculated since the function is not defined by a closed-form expression, but...

Method of undetermined coefficients | Numerical differentiation | Radioactivity migration in Porous medium and MST formula | numerical differentiation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE SCHEMES | RATE CONSTANTS | FLUX | method of undetermined coefficients | radioactivity migration in Porous medium and MST formula | PHYSICS, MATHEMATICAL

Method of undetermined coefficients | Numerical differentiation | Radioactivity migration in Porous medium and MST formula | numerical differentiation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE SCHEMES | RATE CONSTANTS | FLUX | method of undetermined coefficients | radioactivity migration in Porous medium and MST formula | PHYSICS, MATHEMATICAL

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2000, Volume 126, Issue 1, pp. 269 - 276

Conventional numerical differentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simplified to one of the finite...

Taylor series | Finite difference formulas | Closed-form expressions | Numerical differentiation | MATHEMATICS, APPLIED | ACCURATE COMPUTATIONS | closed-form expressions | PHASE-SHIFT PROBLEM | RADIAL SCHRODINGER-EQUATION | EXPONENTIALLY FITTED METHODS | INITIAL-VALUE PROBLEMS | FAMILY | PREDICTOR-CORRECTOR METHODS | numerical differentiation | ORDER METHODS | LAG | INTEGRATION | finite difference formulas

Taylor series | Finite difference formulas | Closed-form expressions | Numerical differentiation | MATHEMATICS, APPLIED | ACCURATE COMPUTATIONS | closed-form expressions | PHASE-SHIFT PROBLEM | RADIAL SCHRODINGER-EQUATION | EXPONENTIALLY FITTED METHODS | INITIAL-VALUE PROBLEMS | FAMILY | PREDICTOR-CORRECTOR METHODS | numerical differentiation | ORDER METHODS | LAG | INTEGRATION | finite difference formulas

Journal Article

Results in Mathematics, ISSN 1422-6383, 2009, Volume 53, Issue 3-4, pp. 445 - 452

We describe certain properties of optimal numerical differentiation formulae.

Modulus of continuity | Lagrange-Hermite interpolation | Optimal numerical differentiation formula | MATHEMATICS | MATHEMATICS, APPLIED | modulus of continuity | Mathematical optimization

Modulus of continuity | Lagrange-Hermite interpolation | Optimal numerical differentiation formula | MATHEMATICS | MATHEMATICS, APPLIED | modulus of continuity | Mathematical optimization

Journal Article

Neurocomputing, ISSN 0925-2312, 10/2014, Volume 142, pp. 165 - 173

In addition to the high-speed parallel-distributed processing property, neural networks can be readily implemented by hardware and thus have been applied...

Numerical-differentiation formula | Time-varying matrix pseudoinverse | Discrete-time Zhang neural network | Motion generation | ITERATION | MOORE-PENROSE INVERSE | OPTIMIZATION | PSEUDO-INVERSE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Neural networks | Control systems

Numerical-differentiation formula | Time-varying matrix pseudoinverse | Discrete-time Zhang neural network | Motion generation | ITERATION | MOORE-PENROSE INVERSE | OPTIMIZATION | PSEUDO-INVERSE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Neural networks | Control systems

Journal Article

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