Optimization Methods and Software, ISSN 1055-6788, 01/2018, Volume 33, Issue 1, pp. 92 - 119

We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing...

block-triangular ordering | nonlinear programming | differential-algebraic equations | tearing | sparsity preservation | dynamic optimization | Modelica | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | DESIGN | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODEL | Tearing | Boundary value problems | Algebra | Sparsity | Preprocessing | Optimal control | Differential equations | Collocation methods | Optimization | Computational Mathematics | Mathematics | Naturvetenskap | Beräkningsmatematik | Natural Sciences | Matematik

block-triangular ordering | nonlinear programming | differential-algebraic equations | tearing | sparsity preservation | dynamic optimization | Modelica | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | DESIGN | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODEL | Tearing | Boundary value problems | Algebra | Sparsity | Preprocessing | Optimal control | Differential equations | Collocation methods | Optimization | Computational Mathematics | Mathematics | Naturvetenskap | Beräkningsmatematik | Natural Sciences | Matematik

Journal Article

Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 9/2018, Volume 42, Issue 3, pp. 1343 - 1350

In this study we propose an efficient technique for approximate solution of linear and nonlinear differential equations with fractional order. The operational...

34G20 | Materials Science, general | 26A33 | Earth Sciences, general | 34A08 | 42C10 | Engineering | Life Sciences, general | Fractional differential equations | Chemistry/Food Science, general | Hybrid function | Operational matrix | Block-pulse function | Engineering, general | Physics, general | Chebyshev polynomials of the second kind | BAGLEY-TORVIK | NUMERICAL-SOLUTION | MULTIDISCIPLINARY SCIENCES | TRANSFORM | COLLOCATION | Functions (mathematics) | Nonlinear equations | Mathematical analysis | Upper bounds | Differential equations | Chebyshev approximation | Polynomials | Matrix methods

34G20 | Materials Science, general | 26A33 | Earth Sciences, general | 34A08 | 42C10 | Engineering | Life Sciences, general | Fractional differential equations | Chemistry/Food Science, general | Hybrid function | Operational matrix | Block-pulse function | Engineering, general | Physics, general | Chebyshev polynomials of the second kind | BAGLEY-TORVIK | NUMERICAL-SOLUTION | MULTIDISCIPLINARY SCIENCES | TRANSFORM | COLLOCATION | Functions (mathematics) | Nonlinear equations | Mathematical analysis | Upper bounds | Differential equations | Chebyshev approximation | Polynomials | Matrix methods

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2011, Volume 34, Issue 2, pp. 379 - 388

System of integral equations have been solved in many papers. In particular, systems of integral equations with degenerate kernels have been solved with...

System of Fredholm integral equations | Collocation method | Legendre polynomials | Adomian's decomposition method | collocation method | MATHEMATICS | NUMERICAL-SOLUTION | BLOCK-PULSE FUNCTIONS | TAYLOR | DIFFERENTIAL-EQUATIONS | CONVERGENCE | HOMOTOPY PERTURBATION METHOD | 2ND KIND

System of Fredholm integral equations | Collocation method | Legendre polynomials | Adomian's decomposition method | collocation method | MATHEMATICS | NUMERICAL-SOLUTION | BLOCK-PULSE FUNCTIONS | TAYLOR | DIFFERENTIAL-EQUATIONS | CONVERGENCE | HOMOTOPY PERTURBATION METHOD | 2ND KIND

Journal Article

ENGINEERING WITH COMPUTERS, ISSN 0177-0667, 04/2020, Volume 36, Issue 2, pp. 795 - 806

The aim of the current paper is to propose an efficient method for finding the approximate solution of fractional delay differential equations. This technique...

NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CHEBYSHEV | Fractional-order Fibonacci-hybrid function | BLOCK-PULSE FUNCTIONS | Fibonacci polynomial | Operational matrix | Collocation method | ENGINEERING, MECHANICAL | Population growth | Basis functions | Mathematical analysis | Differential equations | Collocation methods | Mathematical models | Polynomials | Iterative methods | Delay

NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CHEBYSHEV | Fractional-order Fibonacci-hybrid function | BLOCK-PULSE FUNCTIONS | Fibonacci polynomial | Operational matrix | Collocation method | ENGINEERING, MECHANICAL | Population growth | Basis functions | Mathematical analysis | Differential equations | Collocation methods | Mathematical models | Polynomials | Iterative methods | Delay

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 11/2018, Volume 95, Issue 11, pp. 2287 - 2307

This paper deals with the numerical solution of system of fractional integro-differential equations. In this work, we approximate the unknown functions based...

system of fractional integro-differential equations | Hybrid Bernstein Block-Pulse functions | numerical algorithm | convergence analysis | Gaussian quadrature | 65C20 | 68U20 | 26A33 | Hybrid Bernstein Block–Pulse functions | 65L20 | LEGENDRE | MATRIX | MATHEMATICS, APPLIED | INTEGRO DIFFERENTIAL-EQUATIONS | POLYNOMIALS | ORDER | NUMERICAL-SOLUTION | COLLOCATION METHOD | Operators (mathematics) | Mathematical analysis | Numerical methods | Weight reduction | Differential equations | Collocation methods | Weighting functions

system of fractional integro-differential equations | Hybrid Bernstein Block-Pulse functions | numerical algorithm | convergence analysis | Gaussian quadrature | 65C20 | 68U20 | 26A33 | Hybrid Bernstein Block–Pulse functions | 65L20 | LEGENDRE | MATRIX | MATHEMATICS, APPLIED | INTEGRO DIFFERENTIAL-EQUATIONS | POLYNOMIALS | ORDER | NUMERICAL-SOLUTION | COLLOCATION METHOD | Operators (mathematics) | Mathematical analysis | Numerical methods | Weight reduction | Differential equations | Collocation methods | Weighting functions

Journal Article

SIAM-ASA Journal on Uncertainty Quantification, ISSN 2166-2525, 2015, Volume 3, Issue 1, pp. 1109 - 1135

We apply the tensor train (TT) decomposition to construct the tensor product polynomial chaos expansion (PCE) of a random field, to solve the stochastic...

Karhunen-Loève expansion | Tensor train format | Tensor product methods | Uncertainty quantification | Polynomial chaos expansion | Block cross | Adaptive cross approximation | Stochastic galerkin | DIMENSIONALITY | MATRIX | BREAKING | uncertainty quantification | tensor train format | APPROXIMATION | adaptive cross approximation | polynomial chaos expansion | block cross | CURSE | ALGORITHMS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | COLLOCATION METHOD | stochastic Galerkin | Karhunen-Loeve expansion | SYSTEMS | tensor product methods

Karhunen-Loève expansion | Tensor train format | Tensor product methods | Uncertainty quantification | Polynomial chaos expansion | Block cross | Adaptive cross approximation | Stochastic galerkin | DIMENSIONALITY | MATRIX | BREAKING | uncertainty quantification | tensor train format | APPROXIMATION | adaptive cross approximation | polynomial chaos expansion | block cross | CURSE | ALGORITHMS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | COLLOCATION METHOD | stochastic Galerkin | Karhunen-Loeve expansion | SYSTEMS | tensor product methods

Journal Article

Connection Science, ISSN 0954-0091, 01/2020, Volume 32, Issue 1, pp. 53 - 80

In this paper, we develop a numerical method for solving the delay optimal control problems of fractional-order. The fractional derivatives are considered in...

error function | Delay optimal control problems | optimisation scheme | fractional power series | transfer functions | fractional-order | Padé approximation | Hamiltonian conditions | neural network | OPTIMIZATION PROBLEMS | Pade approximation | BOUNDARY-VALUE-PROBLEMS | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VARIATIONAL ITERATION METHOD | NUMERICAL-SOLUTION | PROGRAMMING PROBLEMS | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | BLOCK-PULSE FUNCTIONS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS

error function | Delay optimal control problems | optimisation scheme | fractional power series | transfer functions | fractional-order | Padé approximation | Hamiltonian conditions | neural network | OPTIMIZATION PROBLEMS | Pade approximation | BOUNDARY-VALUE-PROBLEMS | MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VARIATIONAL ITERATION METHOD | NUMERICAL-SOLUTION | PROGRAMMING PROBLEMS | COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | BLOCK-PULSE FUNCTIONS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Multidiscipline Modeling in Materials and Structures, ISSN 1573-6105, 12/2018, Volume 14, Issue 5, pp. 960 - 969

Purpose The purpose of this paper is to develop a block method of order five for the general solution of the first-order initial value problems for Volterra...

Collocation | Block method | Viscosity | Predictor-corrector methods | Boundary value problems | Approximation | Basis functions | Integrators | Laplace transforms | Researchers | Mathematical analysis | Differential equations | Ordinary differential equations | Mathematical models | Polynomials | Runge-Kutta method | Methods

Collocation | Block method | Viscosity | Predictor-corrector methods | Boundary value problems | Approximation | Basis functions | Integrators | Laplace transforms | Researchers | Mathematical analysis | Differential equations | Ordinary differential equations | Mathematical models | Polynomials | Runge-Kutta method | Methods

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 3297 - 3321

In the current study, a new technique for solving various kinds of fractional partial differential equations based upon Genocchi hybrid functions (GHFs) is...

65M15 | 65M70 | Theoretical, Mathematical and Computational Physics | Caputo derivative | Operational matrix | 35R11 | Mathematics, general | Mathematics | Applications of Mathematics | Genocchi hybrid functions | Collocation method | Fractional partial differential equations | DELAY SYSTEMS | DIFFUSION EQUATIONS | WAVE-FORM RELAXATION | POLYNOMIALS | MATHEMATICS | ORDER | SCHEME | BLOCK-PULSE FUNCTIONS | PARTIAL INTEGRODIFFERENTIAL EQUATIONS | NONLINEAR PDES | Error analysis | Partial differential equations | Sobolev space | Delay

65M15 | 65M70 | Theoretical, Mathematical and Computational Physics | Caputo derivative | Operational matrix | 35R11 | Mathematics, general | Mathematics | Applications of Mathematics | Genocchi hybrid functions | Collocation method | Fractional partial differential equations | DELAY SYSTEMS | DIFFUSION EQUATIONS | WAVE-FORM RELAXATION | POLYNOMIALS | MATHEMATICS | ORDER | SCHEME | BLOCK-PULSE FUNCTIONS | PARTIAL INTEGRODIFFERENTIAL EQUATIONS | NONLINEAR PDES | Error analysis | Partial differential equations | Sobolev space | Delay

Journal Article

30.
Full Text
High-order continuous third derivative formulas with block extensions for y″=f(x, y, y′)

International Journal of Computer Mathematics, ISSN 0020-7160, 09/2013, Volume 90, Issue 9, pp. 1899 - 1914

A class of high-order continuous third derivative formulas (CTDFs) for second-order ordinary differential equations (ODEs) is proposed. The CTDFs are used to...

continuous method | block extension | initial value problems | third derivative | second order | MATHEMATICS, APPLIED | MULTISTEP METHODS | F(X | KUTTA-NYSTROM METHODS | P-STABLE METHODS | EXPLICIT | COLLOCATION METHODS

continuous method | block extension | initial value problems | third derivative | second order | MATHEMATICS, APPLIED | MULTISTEP METHODS | F(X | KUTTA-NYSTROM METHODS | P-STABLE METHODS | EXPLICIT | COLLOCATION METHODS

Journal Article

Journal of Geodesy, ISSN 0949-7714, 6/2012, Volume 86, Issue 6, pp. 393 - 408

The issue of combining high-resolution gravity models, based on observations taken on the Earth surface, with those derived from satellite-only observations is...

GOCE mission | Earth Sciences | Data combination | Collocation | Earth Sciences, general | Geophysics/Geodesy | Space-wise approach | Block diagonal structures | SPACE | GEOCHEMISTRY & GEOPHYSICS | FIELD DETERMINATION | REMOTE SENSING | Geodetics | Satellites | Simulation | Gravity

GOCE mission | Earth Sciences | Data combination | Collocation | Earth Sciences, general | Geophysics/Geodesy | Space-wise approach | Block diagonal structures | SPACE | GEOCHEMISTRY & GEOPHYSICS | FIELD DETERMINATION | REMOTE SENSING | Geodetics | Satellites | Simulation | Gravity

Journal Article

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 05/2010, Volume 26, Issue 3, pp. 647 - 661

A numerical method for solving the high‐order linear differential equations with variable coefficients under the mixed conditions is presented. The method is...

Taylor and Legendre polynomials | Taylor matrix method | differential equations | Taylor and legendre polynomials | Differential equations | MATHEMATICS, APPLIED | BLOCK-PULSE | TERMS | INTEGRODIFFERENTIAL EQUATIONS | FREDHOLM INTEGRAL-EQUATIONS | VARIABLE-COEFFICIENTS | COLLOCATION METHOD | COMBINATORIAL | SYSTEMS | APPROXIMATE SOLUTION

Taylor and Legendre polynomials | Taylor matrix method | differential equations | Taylor and legendre polynomials | Differential equations | MATHEMATICS, APPLIED | BLOCK-PULSE | TERMS | INTEGRODIFFERENTIAL EQUATIONS | FREDHOLM INTEGRAL-EQUATIONS | VARIABLE-COEFFICIENTS | COLLOCATION METHOD | COMBINATORIAL | SYSTEMS | APPROXIMATE SOLUTION

Journal Article

International Journal of Computational Fluid Dynamics, ISSN 1061-8562, 03/2003, Volume 17, Issue 2, pp. 133 - 149

Basis splines (B-splines) are basis functions for piecewise polynomials having a high level of derivative continuity. They possess attractive properties for...

Mass Matrix | Block-structured Grids | Fast Solvers | Incompressible Navier-Stokes Equations | Galerkin And Collocation Methods | B-splines | Galerkin and collocation methods | Block-structured grids | Mass matrix | Incompressible Navier-Stokes equations | Fast solvers | mass matrix | incompressible Navier-Stokes equations | FINITE-DIFFERENCE SCHEMES | CONSISTENT MASS MATRIX | PHYSICS, FLUIDS & PLASMAS | fast solvers | block-structured grids | BOUNDARY-VALUE-PROBLEMS | SEPARABLE ELLIPTIC-EQUATIONS | SEMIIMPLICIT PROJECTION METHODS | DIRECT NUMERICAL-SIMULATION | MECHANICS | NAVIER-STOKES EQUATIONS | LARGE-EDDY SIMULATION | MATRIX DECOMPOSITION ALGORITHMS | VISCOUS INCOMPRESSIBLE-FLOW

Mass Matrix | Block-structured Grids | Fast Solvers | Incompressible Navier-Stokes Equations | Galerkin And Collocation Methods | B-splines | Galerkin and collocation methods | Block-structured grids | Mass matrix | Incompressible Navier-Stokes equations | Fast solvers | mass matrix | incompressible Navier-Stokes equations | FINITE-DIFFERENCE SCHEMES | CONSISTENT MASS MATRIX | PHYSICS, FLUIDS & PLASMAS | fast solvers | block-structured grids | BOUNDARY-VALUE-PROBLEMS | SEPARABLE ELLIPTIC-EQUATIONS | SEMIIMPLICIT PROJECTION METHODS | DIRECT NUMERICAL-SIMULATION | MECHANICS | NAVIER-STOKES EQUATIONS | LARGE-EDDY SIMULATION | MATRIX DECOMPOSITION ALGORITHMS | VISCOUS INCOMPRESSIBLE-FLOW

Journal Article

Numerical Linear Algebra with Applications, ISSN 1070-5325, 07/2000, Volume 7, Issue 5, pp. 275 - 317

Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two‐point boundary value problems for ordinary...

direct algorithms | almost block diagonal systems | multiple shooting methods | boundary value problems | finite difference methods | collocation methods | parallel computing | iterative algorithms | Almost block diagonal systems | Boundary value problems | Parallel computing | Direct algorithms | Collocation methods | Iterative algorithms | Multiple shooting methods | Finite difference methods

direct algorithms | almost block diagonal systems | multiple shooting methods | boundary value problems | finite difference methods | collocation methods | parallel computing | iterative algorithms | Almost block diagonal systems | Boundary value problems | Parallel computing | Direct algorithms | Collocation methods | Iterative algorithms | Multiple shooting methods | Finite difference methods

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2019, Volume 362, pp. 99 - 115

A block lower triangular Toeplitz system arising from the time–space fractional diffusion equation is discussed. For efficient solutions of such the linear...

Block triangular lower Toeplitz matrix | [formula omitted]-[formula omitted] formula | WSGD | Skew-circulant preconditioner | Krylov subspace methods | Fractional differential equations | MATRIX | MATHEMATICS, APPLIED | L2-1(sigma) formula | DIFFERENCE SCHEME | Differential equations | Mathematics - Numerical Analysis

Block triangular lower Toeplitz matrix | [formula omitted]-[formula omitted] formula | WSGD | Skew-circulant preconditioner | Krylov subspace methods | Fractional differential equations | MATRIX | MATHEMATICS, APPLIED | L2-1(sigma) formula | DIFFERENCE SCHEME | Differential equations | Mathematics - Numerical Analysis

Journal Article

Chinese Journal of Polymer Science, ISSN 0256-7679, 4/2018, Volume 36, Issue 4, pp. 488 - 496

Self-consistent field theory (SCFT), as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to...

Polymer Sciences | Condensed Matter Physics | Self-consistent field theory | Chemistry | Characterization and Evaluation of Materials | Industrial Chemistry/Chemical Engineering | Algorithm | Pseudo-spectral | Phase structure | Block copolymer | STATISTICAL-MECHANICS | PHASES | POLYMERS | POLYMER SCIENCE | STABILITY | SEGREGATION | OXIDE) TRIBLOCK COPOLYMERS | SYSTEMS | MORPHOLOGY | Analysis | Block copolymers | Algorithms

Polymer Sciences | Condensed Matter Physics | Self-consistent field theory | Chemistry | Characterization and Evaluation of Materials | Industrial Chemistry/Chemical Engineering | Algorithm | Pseudo-spectral | Phase structure | Block copolymer | STATISTICAL-MECHANICS | PHASES | POLYMERS | POLYMER SCIENCE | STABILITY | SEGREGATION | OXIDE) TRIBLOCK COPOLYMERS | SYSTEMS | MORPHOLOGY | Analysis | Block copolymers | Algorithms

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2006, Volume 44, Issue 3, pp. 1275 - 1296

We propose and examine block- diagonal preconditioned and variants of indefinite preconditioners for block two-by-two generalized saddle-point problems. That...

Linear systems | Approximation | Spectral theory | Navier Stokes equation | Eigenvalues | Eigenvectors | Mathematical vectors | Matrices | Iterative methods | Preconditioning | Generalized saddle-point problems | Eigenvalue bounds | Krylov subspace methods | Saddle-point problems | iterative methods | MATHEMATICS, APPLIED | BLOCK PRECONDITIONERS | APPROXIMATION | generalized saddle-point problems | INDEFINITE LINEAR-SYSTEMS | INEXACT | preconditioning | NAVIER-STOKES EQUATIONS | eigenvalue bounds | PART | FAST ITERATIVE SOLUTION | OPTIMIZATION | point problems

Linear systems | Approximation | Spectral theory | Navier Stokes equation | Eigenvalues | Eigenvectors | Mathematical vectors | Matrices | Iterative methods | Preconditioning | Generalized saddle-point problems | Eigenvalue bounds | Krylov subspace methods | Saddle-point problems | iterative methods | MATHEMATICS, APPLIED | BLOCK PRECONDITIONERS | APPROXIMATION | generalized saddle-point problems | INDEFINITE LINEAR-SYSTEMS | INEXACT | preconditioning | NAVIER-STOKES EQUATIONS | eigenvalue bounds | PART | FAST ITERATIVE SOLUTION | OPTIMIZATION | point problems

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2017, Volume 2017, Issue 1, pp. 1 - 13

In this study, the numerical technique based on two-dimensional block pulse functions (2D-BPFs) has been developed to approximate the solution of fractional...

numerical solution | Ordinary Differential Equations | block pulse functions | error analysis | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | Partial Differential Equations | fractional Poisson type equations | Dirichlet and Neumann boundary conditions | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | TEMPERATURE | PARTIAL-DIFFERENTIAL-EQUATIONS | Boundary value problems | Poisson distribution | Series, Dirichlet | Tests, problems and exercises | Error analysis | Mathematical analysis | Dirichlet problem | Texts | Wavelet analysis | Boundary conditions | Mathematical models

numerical solution | Ordinary Differential Equations | block pulse functions | error analysis | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | Partial Differential Equations | fractional Poisson type equations | Dirichlet and Neumann boundary conditions | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | TEMPERATURE | PARTIAL-DIFFERENTIAL-EQUATIONS | Boundary value problems | Poisson distribution | Series, Dirichlet | Tests, problems and exercises | Error analysis | Mathematical analysis | Dirichlet problem | Texts | Wavelet analysis | Boundary conditions | Mathematical models

Journal Article

Computational and Mathematical Methods, ISSN 2577-7408, 03/2019, Volume 1, Issue 2, pp. e1016 - n/a

A two‐step hybrid block method is developed for numerically solving first‐order initial‐value problems. The formulas will be obtained from a continuous...

hybrid block method | first‐order initial‐value problem | Runge‐Kutta method | A‐stability | efficient reformulation

hybrid block method | first‐order initial‐value problem | Runge‐Kutta method | A‐stability | efficient reformulation