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## High order semi-implicit schemes for time dependent partial differential equations, submitted to Journal of Scientific Computing

Citations: | 1 - 0 self |

### Citations

156 | Implicit-explicit Runge–Kutta methods for timedependent partial differential equations
- Ascher, Ruuth, et al.
- 1997
(Show Context)
Citation Context ...n the literature can be classified in three different types characterized by the structure of the matrix A = (aij) s i,j=1 of the implicit scheme. Following [7], we will rely on the following notions =-=[1, 13, 27]-=-. Definition 2.1. An IMEX Runge-Kutta method is said to be of type A [27] if the matrix A ∈ Rs×s is invertible. It is said to be of type CK [13] if the matrix A ∈ Rs×s can be written in the form A = (... |

81 | The lubrication approximation for thin viscous films: regularity and long time behavior of weak solutions
- Bertozzi, Pugh
- 1996
(Show Context)
Citation Context ... ω ∂3ω ∂x3 ) = 0, x ∈ R, t ≥ 0, with ω(x, t = 0) = ω0(x) ≥ 0. One of the remarkable features of equation (29) is that its nonlinearity guarantees the nonnegativity preserving property of the solution =-=[4]-=- and the conservation of mass∫ R ω(t, x)dx = ∫ R ω0(x)dx. Moreover there is dissipation of surface-tension energy, that is, d dt ∫ R ∣∣∣∣∂ω∂x ∣∣∣∣2 dx = −∫ R ω ∣∣∣∣∂3ω∂x3 ∣∣∣∣2 dx, ha l-0 09 83 92 4,s... |

65 | The mathematics of moving contact lines in thin liquid film,
- Bertozzi
- 1998
(Show Context)
Citation Context ...IMEX-SSP(4,3,3) scheme (26) (Bottom). 3.4. Test 4 - Hele-Shaw flow. In this section we consider a fourth order nonlinear degenerate diffusion equation in one space dimension called the Hele-Shaw cell =-=[3, 28]-=- (29) ∂ω ∂t + ∂ ∂x ( ω ∂3ω ∂x3 ) = 0, x ∈ R, t ≥ 0, with ω(x, t = 0) = ω0(x) ≥ 0. One of the remarkable features of equation (29) is that its nonlinearity guarantees the nonnegativity preserving prope... |

17 | Implicit-Explicit Runge–Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit
- Boscarino, Pareschi, et al.
(Show Context)
Citation Context ...ion, by Jin and Filbet [19] in the context of the Boltzmann equation of rarefied gas dynamics when the Knudsen number is very small, and in the context of hyperbolic systems with diffusive relaxation =-=[6, 9, 11]-=-. Notice that such penalization technique expressed by Eq.4 is a particular case of Eq.(3). The aim of this paper is to propose a new class of semi-implicit schemes based on IMEX Runge-Kutta methods w... |

15 |
Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems
- Boscarino
(Show Context)
Citation Context ...schemes. IMEX Runge-Kutta schemes present in the literature can be classified in three different types characterized by the structure of the matrix A = (aij) s i,j=1 of the implicit scheme. Following =-=[7]-=-, we will rely on the following notions [1, 13, 27]. Definition 2.1. An IMEX Runge-Kutta method is said to be of type A [27] if the matrix A ∈ Rs×s is invertible. It is said to be of type CK [13] if t... |

6 |
Late–time relaxation limits of nonlinear hyperbolic systems. A general framework
- Berthon, LeFloch, et al.
- 2012
(Show Context)
Citation Context ...h are of parabolic type and may contain degenerate and/or fully nonlinear diffusion terms. Fully nonlinear relaxation terms can arise, for instance, in presence of strong friction, see for example in =-=[2]-=- and references therein. Furthermore, a general class of models of the same type were introduced by Kawashima and LeFloch (LeFloch and Kawashima, private communication) and proposed in [6]. For such p... |

5 | On an accurate third order implicit–explicit Runge-Kutta method for stiff problems - Boscarino |

1 |
anf F. Filbet, A finite volume scheme for nonlinear degenerate parabolic equations
- Bessemoulin-Chatard
(Show Context)
Citation Context ...case in any dimension and for 1D boson case by relating the entropy and its dissipation. Here we want to approximate this nonlinear equation and study the long time behavior of the numerical solution =-=[5]-=-. To apply our semi-implicit scheme we rewrite this PDE in the form (3) with u the component treated explicitly, v the component treated implicitly and H(t, u, v) = div (x (1 + k u) v + ∇v) = div (x (... |

1 |
High-order asymtotic-preserving methods for fully non linear relaxation problems
- Boscarino, LeFloch, et al.
(Show Context)
Citation Context ...adopt different semi-implicit schemes, which exploit the structure of the system, resulting in a very effective tool, being a good compromise among accuracy, stability and robustness. For instance in =-=[6]-=-, the authors consider nonlinear hyperbolic systems containing fully nonlinear and stiff relaxation terms in the limit of arbitrary late times. The dynamics is asymptotically governed by effective sys... |