A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients
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DOI: 10.1002/mma.5592
Abstract: We present the Method Of Lines (MOL), which is based on the spectral collocation method, to solve space-fractional advection-diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which… read more here.
Keywords: advection diffusion; collocation method; method;
An indirect convergent Jacobi spectral collocation method for fractional optimal control problems
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DOI: 10.1002/mma.5968
Abstract: In this paper, we present a novel indirect convergent Jacobi spectral collocation method for fractional optimal control problems governed by a dynamical system including both classical derivative and Caputo fractional derivative. First, we present some… read more here.
Keywords: indirect convergent; jacobi spectral; spectral collocation; convergent jacobi ... See more keywords
A mixed DOF collocation method for elastic problems in heterogeneous structure
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DOI: 10.1002/nme.6087
Abstract: In this paper, a collocation method with mixed degrees of freedom (DOFs) is proposed for heterogeneous structures. Local tractions of the outer and interface boundaries are introduced as DOFs in the mixed collocation scheme. Then,… read more here.
Keywords: collocation; stiffness matrix; heterogeneous structure; collocation method ... See more keywords
An hp‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use
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DOI: 10.1002/nme.7234
Abstract: This article introduces an hp$$ hp $$ ‐adaptive multi‐element stochastic collocation method, which additionally allows to re‐use existing model evaluations during either h$$ h $$ ‐ or p$$ p $$ ‐refinement. The collocation method is… read more here.
Keywords: adaptive multi; element stochastic; method; multi element ... See more keywords
A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions
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DOI: 10.1007/s00366-020-00953-9
Abstract: The main purpose of this work is to develop a spectrally accurate collocation method for solving weakly singular integral equations of the second kind with nonsmooth solutions in high dimensions. The proposed spectral collocation method… read more here.
Keywords: method; equations nonsmooth; nonsmooth solutions; integral equations ... See more keywords
Chebyshev–Gauss–Lobatto collocation method for variable-order time fractional generalized Hirota–Satsuma coupled KdV system
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DOI: 10.1007/s00366-020-01125-5
Abstract: In this paper, the Chebyshev–Gauss–Lobatto collocation method is developed for studying the variable-order (VO) time fractional model of the generalized Hirota–Satsuma coupled KdV system arising in interaction of long waves. To define this new system,… read more here.
Keywords: collocation; system; gauss lobatto; chebyshev gauss ... See more keywords
The spectral collocation method for efficiently solving PDEs with fractional Laplacian
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DOI: 10.1007/s10444-017-9564-6
Abstract: We derive a spectral collocation approximation to the fractional Laplacian operator based on the Riemann-Liouville fractional derivative operators on a bounded domain Ω = [a, b]. Corresponding matrix representations of (−△)α/2 for α ∈ (0,1)… read more here.
Keywords: method efficiently; collocation method; spectral collocation; fractional laplacian ... See more keywords
A Legendre collocation method for distributed-order fractional optimal control problems
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DOI: 10.1007/s11071-017-4038-4
Abstract: In many dynamic processes, the fractional differential operators not only appear as discrete fractional, but they also possess a continuous nature in a sense that their order is distributed over a given range. This paper… read more here.
Keywords: distributed order; order; method; order fractional ... See more keywords
An improved collocation method for solving a fractional integro-differential equation
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DOI: 10.1007/s40314-020-01409-y
Abstract: In the paper, an improved collocation method is proposed for solving a linear fractional integro-differential equation. The method is proposed by improving the residual to vanish and require the residual to the minimum in sense… read more here.
Keywords: method; fractional integro; improved collocation; integro differential ... See more keywords
Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method
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DOI: 10.1007/s40430-020-02332-3
Abstract: Natural frequencies and free vibration are important characteristics of beams with non-uniform cross section. Hence, the solution for free vibrations of non-uniform beams is presented using a Laguerre collocation method. The elastically restrained beam model… read more here.
Keywords: non uniform; laguerre collocation; method; beams non ... See more keywords
An Adaptive Collocation Method for Solving Delay Fractional Differential Equations
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DOI: 10.1007/s40819-019-0737-5
Abstract: In this article, an adaptive collocation method is investigated for solving delay fractional differential equations (DFDEs). The fractional derivative is described in the Caputo–Fabrizio sense, that is a new fractional derivative with non-singular kernel. This… read more here.
Keywords: collocation; method; solving delay; adaptive collocation ... See more keywords