A linearization of a backward Euler scheme for a class of degenerate nonlinear advection–diffusion equations

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1097-e1106 ◽  
Author(s):  
Koffi B. Fadimba
Keyword(s):  
Diffusion Equations ◽  
Euler Scheme ◽  
Backward Euler Scheme ◽  
Advection Diffusion ◽  
Backward Euler ◽  
Nonlinear Advection

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 linear backward Euler scheme for a class of degenerate advection–diffusion equations: A mathematical analysis of the convergence in L∞(0, T0;L2(Ω)) and in L2(0, T0;H1(Ω))

2014 ◽  
Vol 12 (03) ◽  
pp. 227-249 ◽  
Author(s):  
Koffi B. Fadimba
Keyword(s):  
Error Estimates ◽  
Regularization Parameter ◽  
Discretization Parameter ◽  
Backward Euler Scheme ◽  
Time Stepping ◽  
Advection Diffusion ◽  
Backward Euler ◽  
Linear Scheme ◽  
Convergence Estimates ◽  
Linearized Scheme

This paper concerns itself with establishing convergence estimates for a linearized scheme for solving numerically the saturation equation. In a previous paper, error estimates were obtained for the same scheme in L2(0, T0;L2(Ω)). In this work, we establish error estimates for the linear scheme in L∞(0, T0;L2(Ω)) and in L2(0, T0;H1(Ω)) (in the discrete norms). Under certain realistic conditions, we show that, if the regularization parameter β and the spatial discretization parameter h are carefully chosen in terms of the time-stepping parameter Δt, the convergence, in these spaces, is at least of order O((Δt)α) for some determined α > 0, function of a parameter μ > 0 defined in the problem. Examples of possible choices of β and h in terms of Δt are given.

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