An explicit spectral collocation method for the linearized Korteweg–de Vries equation on unbounded domain

Fang, Jinwei; Wu, Boying; Liu, Wenjie

doi:10.1016/j.apnum.2017.11.008

Cited by 5 publications

(7 citation statements)

References 19 publications

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“…We now show that the semi-discrete numerical scheme (26) is stable. The proof follows a similar approach as in [13].…”

Section: Stability Of the Semi-discrete Schemementioning

confidence: 98%

“…We assume g(x) constant for x ∈ R \ [a, b] and that u 0 (x) is a smooth initial value with compact support in [a, b]. Transparent boundary conditions are established by considering (13) on the complementary unbounded domain R \ (a, b). Let g a,b be the values of g(x) in (−∞, a] and [b, ∞), respectively.…”

Section: Discrete Transparent Boundary Conditionsmentioning

confidence: 99%

“…The mathematical tool we employ in order to impose discrete transparent boundary conditions to (13) is the Z-transform. We recall the definition and the main properties of the Z-transform, which are used extensively in this section.…”

Section: Discrete Transparent Boundary Conditionsmentioning

confidence: 99%

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A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

2021

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The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov–Galerkin method is considered which gives spectral accuracy. The main difficulty in constructing a second-order splitting scheme in such a situation lies in the compatibility condition at the boundaries of the sub-problems. In particular, the presence of an inflow boundary condition in the advection part results in order reduction. To overcome this issue a modified Strang splitting scheme is introduced that retains second-order accuracy. For this numerical scheme a stability analysis is conducted. In addition, numerical results are shown to support the theoretical derivations.

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“…We now show that the semi-discrete numerical scheme (26) is stable. The proof follows a similar approach as in [13].…”

Section: Stability Of the Semi-discrete Schemementioning

confidence: 98%

Section: Discrete Transparent Boundary Conditionsmentioning

confidence: 99%

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A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

2021

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show abstract

“…We now show that the semi-discrete numerical scheme (26) is stable. The proof follows a similar approach as in [11].…”

Section: Stability Of the Semi-discrete Schemementioning

confidence: 98%

“…Notice that g * (a) = g * (b) = 0. This means that no inflow or outflow condition needs to be prescribed to Equation (11). The modified splitting allows us to solve the advection equation only for the interior points, i.e.…”

Section: Modified Splittingmentioning

confidence: 99%

A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

Einkemmer¹,

Ostermann²,

Residori³

2020

Preprint

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The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov-Galerkin method is considered which gives spectral accuracy. The main difficulty in constructing a second-order splitting scheme in such a situation lies in the compatibility condition at the boundaries of the sub-problems. In particular, the presence of an inflow boundary condition in the advection part results in order reduction. To overcome this issue a modified Strang splitting scheme is introduced that retains second-order accuracy. For this numerical scheme a stability analysis is conducted. In addition, numerical results are shown to support the theoretical derivations.

show abstract

A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions

Einkemmer

Ostermann

Residori

2021

Journal of Computational and Applied Mathematics

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An explicit spectral collocation method for the linearized Korteweg–de Vries equation on unbounded domain

Cited by 5 publications

References 19 publications

A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions

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