Engineering with computers, ISSN 1435-5663, 12/2018, Volume 35, Issue 4, pp. 1391 - 1408

.... To handle the method, we first convert these types of differential equations to linear fractional Volterra integral equations of the second kind...

Discrete collocation method | Error analysis | Systems Theory, Control | Classical Mechanics | Thin plate spline | 34A08 | Fractional differential equation | 45E99 | 41A25 | Calculus of Variations and Optimal Control; Optimization | Computer-Aided Engineering (CAD, CAE) and Design | Computer Science | Mathematical and Computational Engineering | Volterra integral equation | 45D05 | Math. Applications in Chemistry | Engineering | Computer Science, Interdisciplinary Applications | Technology | Engineering, Mechanical | Science & Technology | Basis functions | Splines | Fractional calculus | Finite element method | Radial basis function | Integral equations | Meshless methods | Differential equations | Collocation methods | Reliability analysis | Thin plates | Volterra integral equations

Discrete collocation method | Error analysis | Systems Theory, Control | Classical Mechanics | Thin plate spline | 34A08 | Fractional differential equation | 45E99 | 41A25 | Calculus of Variations and Optimal Control; Optimization | Computer-Aided Engineering (CAD, CAE) and Design | Computer Science | Mathematical and Computational Engineering | Volterra integral equation | 45D05 | Math. Applications in Chemistry | Engineering | Computer Science, Interdisciplinary Applications | Technology | Engineering, Mechanical | Science & Technology | Basis functions | Splines | Fractional calculus | Finite element method | Radial basis function | Integral equations | Meshless methods | Differential equations | Collocation methods | Reliability analysis | Thin plates | Volterra integral equations

Journal Article

01/2019, ISBN 3038976679

.... The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features...

structured matrices | curl | numerical methods | time fractional differential equations | hierarchical splines | finite difference methods | null-space | highly oscillatory problems | stochastic Volterra integral equations | differential equations | displacement rank | constrained Hamiltonian problems | Hermite | hyperbolic partial differential equations | higher-order finite element methods | continuous geometric average | Volterra integro | spectral (eigenvalue) and singular value distributions | generalized locally Toeplitz sequences | Obreshkov methods | B-spline | discontinuous Galerkin methods | adaptive methods | Cholesky factorization | energy-conserving methods | order | collocation method | Poisson problems | time harmonic Maxwell’s equations and magnetostatic problems | tree | multistep methods | stochastic differential equations | optimal basis | finite difference method | elementary differential | gradient system | Runge | conservative problems | line integral methods | stochastic multistep methods | Hamiltonian Boundary Value Methods | Kutta | limited memory | boundary element method | convergence | analytical solution | preconditioners | asymptotic stability | collocation methods | histogram specification | local refinement | edge-preserving smoothing | numerical analysis | THB-splines | BS methods | barrier options | stump | shock waves and discontinuities | mean-square stability | Volterra integral equations | high order discontinuous Galerkin finite element schemes | B-splines | vectorization and parallelization | initial value problems | one-step methods | scientific computing | fractional derivative | linear systems | Hamiltonian problems | low rank completion | ordinary differential equations | mixed-index problems | edge-histogram | Hamiltonian PDEs | matrix ODEs | HBVMs | floating strike Asian options | generalized Schur algorithm | Galerkin method | symplecticity | high performance computing | isogeometric analysis | discretization of systems of differential equations | curl operator

structured matrices | curl | numerical methods | time fractional differential equations | hierarchical splines | finite difference methods | null-space | highly oscillatory problems | stochastic Volterra integral equations | differential equations | displacement rank | constrained Hamiltonian problems | Hermite | hyperbolic partial differential equations | higher-order finite element methods | continuous geometric average | Volterra integro | spectral (eigenvalue) and singular value distributions | generalized locally Toeplitz sequences | Obreshkov methods | B-spline | discontinuous Galerkin methods | adaptive methods | Cholesky factorization | energy-conserving methods | order | collocation method | Poisson problems | time harmonic Maxwell’s equations and magnetostatic problems | tree | multistep methods | stochastic differential equations | optimal basis | finite difference method | elementary differential | gradient system | Runge | conservative problems | line integral methods | stochastic multistep methods | Hamiltonian Boundary Value Methods | Kutta | limited memory | boundary element method | convergence | analytical solution | preconditioners | asymptotic stability | collocation methods | histogram specification | local refinement | edge-preserving smoothing | numerical analysis | THB-splines | BS methods | barrier options | stump | shock waves and discontinuities | mean-square stability | Volterra integral equations | high order discontinuous Galerkin finite element schemes | B-splines | vectorization and parallelization | initial value problems | one-step methods | scientific computing | fractional derivative | linear systems | Hamiltonian problems | low rank completion | ordinary differential equations | mixed-index problems | edge-histogram | Hamiltonian PDEs | matrix ODEs | HBVMs | floating strike Asian options | generalized Schur algorithm | Galerkin method | symplecticity | high performance computing | isogeometric analysis | discretization of systems of differential equations | curl operator

eBook

Journal of computational and nonlinear dynamics, ISSN 1555-1415, 09/2016, Volume 11, Issue 5

In this paper, a numerical method for solving the fractional Bagley-Torvik equation is given...

fractional integral operator | Riemann-Liouville fractional integral | Bagley-Torvik equations | fractional Taylor | operational matrix | Caputo derivative | Mechanics | Engineering | Technology | Engineering, Mechanical | Science & Technology | Nonlinear dynamics | Numerical analysis | Algebra | Approximation | Computation | Mathematical analysis | Mathematical models | Vectors (mathematics)

fractional integral operator | Riemann-Liouville fractional integral | Bagley-Torvik equations | fractional Taylor | operational matrix | Caputo derivative | Mechanics | Engineering | Technology | Engineering, Mechanical | Science & Technology | Nonlinear dynamics | Numerical analysis | Algebra | Approximation | Computation | Mathematical analysis | Mathematical models | Vectors (mathematics)

Journal Article

Nonlinear Engineering, ISSN 2192-8010, 09/2018, Volume 7, Issue 3, pp. 163 - 169

.... B-spline wavelet method has been developed to approximate the solution of Hammerstein integral equation...

Scaling and Wavelet functions | Hammerstein integral equation | B-spline | Multiresolution analysis | Organic chemistry | Adiabatic flow | Integral equations | Differential equations | Exothermic reactions | Ordinary differential equations | Boundary conditions | Chemical reactions | Wavelet analysis | Mathematical models | Chemical reactors

Scaling and Wavelet functions | Hammerstein integral equation | B-spline | Multiresolution analysis | Organic chemistry | Adiabatic flow | Integral equations | Differential equations | Exothermic reactions | Ordinary differential equations | Boundary conditions | Chemical reactions | Wavelet analysis | Mathematical models | Chemical reactors

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 2008, Volume 46, Issue 4, pp. 1799 - 1820

A discrete method of accuracy $O(h^m )$ is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have weak diagonal and boundary singularities...

Interpolation | Approximation | Singular integral equations | Entire functions | Differential equations | Polynomials | Mathematical functions | Coefficients | Data smoothing | Degrees of polynomials | Weakly singular integral equations | Nyström-type methods | Spline quasi-interpolation | Spline interpolation | Boundary singularities | Product integration methods | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Interpolation | Approximation | Singular integral equations | Entire functions | Differential equations | Polynomials | Mathematical functions | Coefficients | Data smoothing | Degrees of polynomials | Weakly singular integral equations | Nyström-type methods | Spline quasi-interpolation | Spline interpolation | Boundary singularities | Product integration methods | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Computational Mechanics, ISSN 0178-7675, 2/2019, Volume 63, Issue 2, pp. 181 - 199

A novel regularized interface integral equation for three-dimensional steady state heat conduction problems with non-homogeneous inclusions is developed...

Heat conduction | Engineering | Radial integration method | Classical and Continuum Physics | Regularized interface integral equation | Theoretical and Applied Mechanics | Computational Science and Engineering | Inclusion problems | NURBS | Mathematics, Interdisciplinary Applications | Mechanics | Physical Sciences | Mathematics | Technology | Science & Technology

Heat conduction | Engineering | Radial integration method | Classical and Continuum Physics | Regularized interface integral equation | Theoretical and Applied Mechanics | Computational Science and Engineering | Inclusion problems | NURBS | Mathematics, Interdisciplinary Applications | Mechanics | Physical Sciences | Mathematics | Technology | Science & Technology

Journal Article

Numerical Algorithms, ISSN 1017-1398, 3/2013, Volume 62, Issue 3, pp. 445 - 468

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI...

Algorithms | Algebra | Collocation | Integral equations | Numerical Analysis | Computer Science | Numeric Computing | Spline quasi-interpolant | Theory of Computation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Error analysis | Approximation | Rectangles | Splines | Mathematical analysis | Mathematical models | Two dimensional

Algorithms | Algebra | Collocation | Integral equations | Numerical Analysis | Computer Science | Numeric Computing | Spline quasi-interpolant | Theory of Computation | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Error analysis | Approximation | Rectangles | Splines | Mathematical analysis | Mathematical models | Two dimensional

Journal Article

Mathematics and computers in simulation, ISSN 0378-4754, 06/2020, Volume 172, pp. 213 - 223

... Love’s integral equation u(x)+∫−11dπd2+(x−t)2u(t)dt=1,x∈[−1,1],where d>0 is a very small parameter...

Product integration method | Love’s integral equation | Spline quasi-interpolation | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Mathematics | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology

Product integration method | Love’s integral equation | Spline quasi-interpolation | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Mathematics | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology

Journal Article

Numerical algorithms, ISSN 1572-9265, 04/2013, Volume 65, Issue 4, pp. 723 - 743

In this paper, the piecewise polynomial collocation methods are used for solving the fractional integro-differential equations with weakly singular kernels...

Fractional integro-differential equation | Algorithms | Algebra | Numerical Analysis | Computer Science | Numeric Computing | Spline space | Theory of Computation | Volterra integral equation | Collocation method | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Methods | Differential equations | Kernels | Mathematical analysis | Collocation methods | Mathematical models | Transformations | Polynomials | Optimization | Convergence

Fractional integro-differential equation | Algorithms | Algebra | Numerical Analysis | Computer Science | Numeric Computing | Spline space | Theory of Computation | Volterra integral equation | Collocation method | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Methods | Differential equations | Kernels | Mathematical analysis | Collocation methods | Mathematical models | Transformations | Polynomials | Optimization | Convergence

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 04/2018, Volume 331, pp. 327 - 342

This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations...

Singular integrals | Symmetric Galerkin Boundary Element Method (SGBEM) | Isogeometric Analysis (IgA) | Weighted quadrature rules | Boundary Integral Equations (BIEs) | Modified moments | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Computer science | Immunoglobulin A | Analysis | Mathematics - Numerical Analysis

Singular integrals | Symmetric Galerkin Boundary Element Method (SGBEM) | Isogeometric Analysis (IgA) | Weighted quadrature rules | Boundary Integral Equations (BIEs) | Modified moments | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Computer science | Immunoglobulin A | Analysis | Mathematics - Numerical Analysis

Journal Article

Mathematics and computers in simulation, ISSN 0378-4754, 07/2017, Volume 137, pp. 148 - 158

In this paper, we study a numerical solution for semi-explicit integral–algebraic equations. Continuous collocation method for solving such equations numerically is developed...

Third kind integral–algebraic equations | Continuous collocation method | Polynomial spline space

Third kind integral–algebraic equations | Continuous collocation method | Polynomial spline space

Journal Article

IEEE transactions on antennas and propagation, ISSN 1558-2221, 01/2020, Volume 68, Issue 1, pp. 593 - 597

We discuss numerical experiments to compare an isogeometric discretization of the electric field integral equation and a parametric Raviart-Thomas approach...

boundary element method | Boats | electric field integral equation (EFIE) | Raviart–Thomas | Geometry | electric wave equation | Integral equations | Toy manufacturing industry | method of moments | Splines (mathematics) | Electric fields | B-splines | isogeometric analysis | Engineering, Electrical & Electronic | Engineering | Telecommunications | Technology | Science & Technology

boundary element method | Boats | electric field integral equation (EFIE) | Raviart–Thomas | Geometry | electric wave equation | Integral equations | Toy manufacturing industry | method of moments | Splines (mathematics) | Electric fields | B-splines | isogeometric analysis | Engineering, Electrical & Electronic | Engineering | Telecommunications | Technology | Science & Technology

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 03/2021, Volume 384, p. 113153

In this paper, the n-dimensional stochastic Itô-Volterra integral equation is numerically solved via quintic B-spline collocation method...

Itô approximation | Stochastic Itô-Volterra integral equation | Gauss–Legendre quadrature rule | Quintic B-spline interpolation | Convergence analysis

Itô approximation | Stochastic Itô-Volterra integral equation | Gauss–Legendre quadrature rule | Quintic B-spline interpolation | Convergence analysis

Journal Article

International journal of computational methods, ISSN 0219-8762, 12/2012, Volume 9, Issue 4, pp. np - np

This article presents some theoretical results for polynomial spline collocation solution to a new class of semi-explicit Integral Algebraic Equations (IAEs...

spline collocation method | Integral algebraic equation | index of IAEs | system of Volterra integral equation | error analysis | numerical treatment | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology | Algebra | Collocation | Integrals | Mathematical analysis | Splines | Collocation methods | Mathematical models | Convergence

spline collocation method | Integral algebraic equation | index of IAEs | system of Volterra integral equation | error analysis | numerical treatment | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology | Algebra | Collocation | Integrals | Mathematical analysis | Splines | Collocation methods | Mathematical models | Convergence

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2018, Volume 333, pp. 74 - 86

... –Volterra integral equations. The method is based on a combination of the successive approximations method, the linear spline interpolation and Itô approximation...

Stochastic Volterra integral equations | Brownian motion process | Itô integral | Linear spline interpolation | Successive approximations method | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Stochastic Volterra integral equations | Brownian motion process | Itô integral | Linear spline interpolation | Successive approximations method | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 01/2020, Volume 363, pp. 426 - 443

The paper is concerned with the wavelet-Galerkin method for the numerical solution of Fredholm linear integral equations and second-order integro-differential equations...

Wavelet | Quadratic spline | Galerkin method | Integral equation | Integro-differential equation | Short support | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Methods | Differential equations

Wavelet | Quadratic spline | Galerkin method | Integral equation | Integro-differential equation | Short support | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Methods | Differential equations

Journal Article