scholarly journals Convergence to equilibrium for the backward Euler scheme and applications

2010 ◽  
Vol 9 (3) ◽  
pp. 685-702 ◽  
Author(s):  
Benoît Merlet ◽  
◽  
Morgan Pierre ◽  
Keyword(s):  
Convergence To Equilibrium ◽  
Euler Scheme ◽  
Backward Euler Scheme ◽  
Backward Euler

scholarly journals Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift

2020 ◽  
Vol 25 (6) ◽  
pp. 1059-1078
Author(s):  
Kęstutis Kubilius
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Euler Scheme ◽  
Hurst Index ◽  
Unique Positive Solution ◽  
Backward Euler Scheme ◽  
Asymptotically Normal ◽  
Backward Euler ◽  
Locally Lipschitz ◽  
Strongly Consistent

Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.

A second order numerical method for a class of parameterized singular perturbation problems on adaptive grid

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
D. Shakti ◽  
J. Mohapatra
Keyword(s):  
Adaptive Grid ◽  
Richardson Extrapolation ◽  
Euler Scheme ◽  
Backward Euler Scheme ◽  
Monitor Function ◽  
Backward Euler ◽  
The Stability ◽  
Perturbation Problems ◽  
Equidistribution Principle ◽  
Richardson Extrapolation Technique

AbstractA nonlinear singularly perturbed boundary value problem depending on a parameter is considered. First, we solve the problem using the backward Euler finite difference scheme on an adaptive grid. The adaptive grid is a special nonuniform mesh generated through equidistribution principle by a positive monitor function depending on the solution. The behavior of the solution, the stability and the error estimates are discussed. Then, the Richardson extrapolation technique is applied to improve the accuracy of the computed solution associated to the backward Euler scheme. The proofs of the uniform convergence for the backward Euler scheme and the Richardson extrapolation are carried out. Numerical experiments validate the theoretical estimates and indicates that the estimates are sharp.

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