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Stochastic Processes and their Applications, ISSN 0304-4149, 05/2020, Volume 130, Issue 5, pp. 2675 - 2692
In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox–Ingersoll–Ross model driven by fractional Brownian... 
Cox–Ingersoll–Ross model | Optimal strong convergence rate | Malliavin calculus | Fractional Brownian motion | Backward Euler scheme | DISCRETIZATION | APPROXIMATION | Cox-Ingersoll-Ross model | SDES | STATISTICS & PROBABILITY | CIR
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2015, Volume 282, pp. 44 - 53
This paper is a continuation of our previous paper, in which, the second author, with Mao and Szpruch examined the almost sure stability of the Euler–Maruyama... 
Monotone-type condition | Stochastic delay differential equations | Exponential stability | Backward Euler–Maruyama method | Almost sure stability | Backward Euler-Maruyama method | MATHEMATICS, APPLIED | NUMERICAL-SOLUTIONS | Backward Euler Maruyama method | ASYMPTOTIC STABILITY | DISCRETIZATIONS | Differential equations
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2015, Volume 278, pp. 258 - 277
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2018, Volume 336, pp. 8 - 29
This paper examines convergence and stability of the two classes of theta-Milstein schemes for stochastic differential equations (SDEs) with non-global... 
Exponential mean-square stability | SDEs | Split-step theta-Milstein scheme | Stochastic theta-Milstein scheme | Strong convergence rate | MATHEMATICS, APPLIED | APPROXIMATIONS | TIME | RATES | BACKWARD EULER | MEAN-SQUARE STABILITY | SYSTEMS | DIFFUSION | LIPSCHITZ CONTINUOUS COEFFICIENTS | Differential equations
Journal Article
Computational Methods in Applied Mathematics, ISSN 1609-4840, 04/2017, Volume 17, Issue 2, pp. 237 - 252
We introduce and analyze a discontinuous Petrov–Galerkin method with optimal test functions for the heat equation. The scheme is based on the backward Euler... 
Backward Euler Scheme | Rothe’s Method | 65M15 | DPG Method with Optimal Test Functions | Least Squares Method | Ultra-Weak Formulation | 65M60 | Parabolic Problem | 65M12 | Heat Equation | Rothe's Method | MATHEMATICS, APPLIED | Rothe ' s Method | DOMINATED DIFFUSION-PROBLEMS | PROBLEMS II | SQUARES GALERKIN METHODS | PARABOLIC PROBLEMS | Test procedures | Galerkin method
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2014, Volume 244, pp. 361 - 374
Journal Article
by Barth, A and Lang, A
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, ISSN 0304-4149, 05/2013, Volume 123, Issue 5, pp. 1563 - 1587
In this paper, L-P convergence and almost sure convergence of the Milstein approximation of a partial differential equation of advection-diffusion type driven... 
Advection-diffusion equation | EVOLUTION EQUATIONS | Almost sure convergence | APPROXIMATION | INEQUALITY | FINITE-ELEMENT METHODS | CONVOLUTIONS | STATISTICS & PROBABILITY | Stochastic partial differential equation | DRIVEN | Milstein scheme | ADDITIVE NOISE | Galerkin method | L-P convergence | Finite Element method | Backward Euler scheme | Differential equations
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2016, Volume 54, Issue 4, pp. 2323 - 2358
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 05/2013, Volume 123, Issue 5, pp. 1563 - 1587
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 09/2016, Volume 50, Issue 5, pp. 1523 - 1560
We propose a space semi-discrete and a fully discrete finite element scheme for the modified phase field crystal equation (MPFC). The space discretization is... 
Finite elements | Gradient-like systems | Second-order schemes | Łojasiewicz inequality | MATHEMATICS, APPLIED | MODELS | CAHN-HILLIARD EQUATION | DIFFERENCE SCHEME | BACKWARD EULER SCHEME | EQUILIBRIUM | GROWTH | Lojasiewicz inequality | second-order schemes | gradient-like systems | Finite element method | Galerkin method | Discretization | Computer simulation | Convergence
Journal Article
EVOLUTION EQUATIONS AND CONTROL THEORY, ISSN 2163-2480, 06/2019, Volume 8, Issue 2, pp. 315 - 342
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert-Schmidt operators existence of... 
MATHEMATICS | MATHEMATICS, APPLIED | weak solution | backward Euler method | semi-definite data | well-posedness | convergence | Hilbert-Schmidt operator | Riccati differential equation | BOUNDARY CONTROL PROBLEM
Journal Article
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