One-step explicit methods for the numerical integration of perturbed oscillators

2011 ◽  
Vol 88 (15) ◽  
pp. 3324-3334
Author(s):  
Qinghong Li
Keyword(s):  
Numerical Integration ◽  
Explicit Methods ◽  
One Step

Numerical Integration of Some Stiff Constitutive Models of Inelastic Deformation

1980 ◽  
Vol 102 (1) ◽  
pp. 92-96 ◽  
Author(s):  
Virendra Kumar ◽  
Mahesh Morjaria ◽  
Subrata Mukherjee
Keyword(s):  
Numerical Integration ◽  
Inelastic Deformation ◽  
Time Integration ◽  
Constitutive Models ◽  
Integration Scheme ◽  
Uniaxial Deformation ◽  
Time Step ◽  
One Step ◽  
Numerical Time Integration ◽  
Step Control

Several strategies for numerical time-integration of some stiff constitutive models of inelastic deformation are presented in this paper. Numerical results and comparisons are presented for the integration of one such model for the case of uniaxial deformation under various prescribed histories of stress or strain. A simple one step Euler type integration scheme with automatic time-step control, which can be easily adapted to the solution of multiaxial boundary value problems, appears promising.

Closed Newton-Cotes Trigonometrically-Fitted Formulae for Numerical Integration of the Schrödinger Equation

2007 ◽  
Vol 3 (1) ◽  
pp. 45-57 ◽  
Author(s):  
T.E. Simos
Keyword(s):  
Numerical Integration ◽  
Symplectic Geometry ◽  
Efficient Solution ◽  
Symplectic Integrators ◽  
Multilayer Structures ◽  
Symplectic Methods ◽  
One Dimensional ◽  
One Step ◽  
Differential Methods ◽  
Symplectic Schemes

In this paper we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted differential methods, symplectic integrators and efficient solution of the Schr¨odinger equation. Several one step symplectic integrators have been produced based on symplectic geometry, as one can see from the literature. However, the study of multistep symplectic integrators is very poor. Zhu et. al. [1] has studied the symplectic integrators and the well known open Newton-Cotes differential methods and as a result has presented the open Newton-Cotes differential methods as multilayer symplectic integrators. The construction of multistep symplectic integrators based on the open Newton-Cotes integration methods was investigated by Chiou and Wu [2]. In this paper we investigate the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. We also develop trigonometrically-fitted symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes to the well known one-dimensional Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems.

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