The space–time Sinc‐Gallerkin method for parabolic problems

Lewis, D.L.; Lund, John; Bowers, Kenneth L.

doi:10.1002/nme.1620240903

Cited by 29 publications

(11 citation statements)

References 11 publications

(3 reference statements)

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“…The Sinc-Galerkin method for partial differential equations has previously been developed for the model elliptic equation in two dimensions [1,9], the parabolic equation in one dimension [7], and the second order hyperbolic equation in one dimension [11]. The present paper extends the method to the steady state problem in three dimensions and the time dependent problems in at least two.…”

Section: Introductionmentioning

confidence: 93%

The Sinc method in multiple space dimensions: Model problems

1989

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Summary. The Sinc-Galerkin method is applied to the canonical forms of second order partial differential equations in multiple space dimensions. For time dependent problems the scheme is fully Galerkin; i.e., the domain of the basis elements includes time. Hence the approximate solution for each equation is specified by solving the associated linear system. Notation is developed which facilitates description of both the linear systems and the algorithms used to solve them. Alternative algorithms are offered dependent on a scalar versus vector computing environment. Numerical results for the test problems presented sustain the exponential convergence rate of the method even in the presence of singularities.

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Section: Introductionmentioning

confidence: 93%

The Sinc method in multiple space dimensions: Model problems

1989

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“…The approximate solution w a (z, t) can be written in the separated form 7) and the basis functions * j (z) are…”

Section: Solving the Problem With Time-dependent Boundary Conditionsmentioning

confidence: 99%

The fully Sinc‐Galerkin method for time‐dependent boundary conditions

Koonprasert

Bowers

2004

Numerical Methods Partial

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The fully Sinc-Galerkin method is developed for a family of complex-valued partial differential equations with time-dependent boundary conditions. The Sinc-Galerkin discrete system is formulated and represented by a Kronecker product form of those equations. The numerical solution is efficiently calculated and the method exhibits an exponential convergence rate. Several examples, some with a real-valued solution and some with a complex-valued solution, are used to demonstrate the performance of this method.

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“…Moreover, some spectral methods for time discretization of PDEs have been developed rapidly, see, e.g., [2,3,11,27,30,31,[40][41][42][43]. Recently, Guo et al [18,19,45] developed several Legendre-Gauss-type spectral collocation methods for ODEs.…”

Section: Introductionmentioning

confidence: 98%

A Chebyshev-Gauss Spectral Collocation Method for Odrinary Differential Equations

Zhongqing¹

2015

JCM

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In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.Mathematics subject classification: 65L05, 65L60, 41A10.

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The space–time Sinc‐Gallerkin method for parabolic problems

Cited by 29 publications

References 11 publications

The Sinc method in multiple space dimensions: Model problems

The Sinc method in multiple space dimensions: Model problems

The fully Sinc‐Galerkin method for time‐dependent boundary conditions

A Chebyshev-Gauss Spectral Collocation Method for Odrinary Differential Equations

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