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   Articles with "spectral collocation" as a keyword



Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

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recommendations! Published in 2024 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.10263

Abstract: In this study, we utilize a specific combination of orthogonal Gegenbauer polynomials as basis functions that satisfy homogeneous boundary conditions in the spatial variable and homogeneous initial conditions in the temporal variable. We derive an… read more here.

Keywords: spectral collocation; gegenbauer; fisher; collocation gegenbauer ... See more keywords

An indirect convergent Jacobi spectral collocation method for fractional optimal control problems

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recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

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

Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations

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recommendations! Published in 2021 at "Engineering With Computers"

DOI: 10.1007/s00366-020-01263-w

Abstract: This paper presents a spectral collocation technique to solve fractional stochastic Volterra integro-differential equations (FSV-IDEs). The algorithm is based on shifted fractional order Legendre orthogonal functions generated by Legendre polynomials. The shifted fractional order Legendre–Gauss–Radau… read more here.

Keywords: shifted fractional; collocation technique; fractional stochastic; collocation ... See more keywords
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The spectral collocation method for efficiently solving PDEs with fractional Laplacian

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recommendations! Published in 2018 at "Advances in Computational Mathematics"

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

Spectral collocation method for weakly singular Volterra integro-differential equations

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recommendations! Published in 2019 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2019.04.011

Abstract: Abstract Spectral collocation methods are developed for weakly singular Volterra integro-differential equations (VIDEs). Convergence analysis results show that global convergence order depends on the regularities of the kernels functions and solutions to VIDEs, and the… read more here.

Keywords: integro differential; singular volterra; volterra integro; weakly singular ... See more keywords

Spectral collocation method for transient thermal analysis of coupled conductive, convective and radiative heat transfer in the moving plate with temperature dependent properties and heat generation

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recommendations! Published in 2017 at "International Journal of Heat and Mass Transfer"

DOI: 10.1016/j.ijheatmasstransfer.2017.06.082

Abstract: Abstract The spectral collocation method is developed and formulated to solve transient thermal process in the moving plate with temperature dependent properties and heat generation. In this moving plate, thermal conductivity and surface emissivity are… read more here.

Keywords: temperature; collocation; heat; collocation method ... See more keywords
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A general spectral collocation method for computing the dispersion relations of guided acoustic waves in multilayer dissipative structures

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recommendations! Published in 2025 at "Journal of Applied Physics"

DOI: 10.1063/5.0242405

Abstract: A spectral collocation method is proposed to compute the complex wavenumber–real frequency dispersion relations of guided acoustic waves in multilayer structures involving dissipative materials. The nature of these dissipative materials is initially considered to be… read more here.

Keywords: method; relations guided; collocation method; spectral collocation ... See more keywords

Space–time spectral collocation method for one-dimensional PDE constrained optimisation

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recommendations! Published in 2020 at "International Journal of Control"

DOI: 10.1080/00207179.2018.1501161

Abstract: This paper solves an optimal control problem governed by a parabolic PDE. Using Lagrangian multipliers, necessary conditions are derived and then space–time spectral collocation method is applied to discretise spatial derivatives and time derivatives. This… read more here.

Keywords: space time; time; time spectral; collocation method ... See more keywords