The Direct Richardson pth Order (DRp) Schemes: A New Class of Time Integration Schemes for Stochastic Differential Equations

2012 ◽  
Vol 34 (1) ◽  
pp. A137-A160
Author(s):  
Pavel P. Popov ◽  
Stephen B. Pope
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Time Integration ◽  
New Class ◽  
Integration Schemes ◽  
Time Integration Schemes

scholarly journals A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Hendrik Ranocha ◽  
Jan Nordström
Keyword(s):  
Collocation Method ◽  
Initial Conditions ◽  
Time Integration ◽  
Initial Condition ◽  
Integration Methods ◽  
Summation By Parts ◽  
New Class ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Time Integration Methods

AbstractSince integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical methods. This article contributes to this topic by proposing a novel class of A stable SBP time integration methods which can also be reformulated as implicit Runge-Kutta methods. In contrast to existing SBP time integration methods using simultaneous approximation terms to impose the initial condition weakly, the new schemes use a projection method to impose the initial condition strongly without destroying the SBP property. The new class of methods includes the classical Lobatto IIIA collocation method, not previously formulated as an SBP scheme. Additionally, a related SBP scheme including the classical Lobatto IIIB collocation method is developed.

scholarly journals Damaged behavior under plane stress

2011 ◽  
pp. 341-368
Author(s):  
Thomas Paris ◽  
Khémaïs Saanouni
Keyword(s):  
Plane Stress ◽  
Constitutive Equations ◽  
Stress Condition ◽  
Time Integration ◽  
Reference Case ◽  
Plane Stress Condition ◽  
Integration Schemes ◽  
Hyperbolic Sine ◽  
Time Integration Schemes ◽  
Fully Coupled

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.

3D nonlinear MHD calculations using implicit and explicit time integration schemes

1986 ◽  
Vol 65 (2) ◽  
pp. 253-272 ◽  
Author(s):  
L. Garcia ◽  
H.R. Hicks ◽  
B.A. Carreras ◽  
L.A. Charlton ◽  
J.A. Holmes
Keyword(s):  
Time Integration ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Implicit And Explicit
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