The Experts below are selected from a list of 87 Experts worldwide ranked by ideXlab platform
Mattias Sandberg - One of the best experts on this subject based on the ideXlab platform.
-
the Forward Euler scheme for nonconvex lipschitz differential inclusions converges with rate one
arXiv: Numerical Analysis, 2009Co-Authors: Mattias SandbergAbstract:In a previous paper it was shown that the Forward Euler Method applied to differential inclusions where the right-hand side is a Lipschitz continuous set-valued function with uniformly bounded, com- pact values, converges with rate one. The convergence, which was there in the sense of reachable sets, is in this paper strengthened to the sense of convergence of solution paths. An improvement of the error constant is given for the case when the set-valued function consists of a small number of smooth ordinary functions.
-
convergence of the Forward Euler Method for nonconvex differential inclusions
SIAM Journal on Numerical Analysis, 2008Co-Authors: Mattias SandbergAbstract:The convergence of reachable sets for nonconvex differential inclusions is considered. When the right-hand side in the differential inclusion is a compact-valued, Lipschitz continuous set-valued function it is shown that the convergence in Hausdorff distance of reachable sets for a Forward Euler discretization is linear in the time step.
Sania Qureshi - One of the best experts on this subject based on the ideXlab platform.
-
two strain epidemic model involving fractional derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the fractional version with respect to the Atangana-Baleanu fractional derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its fractional version is not possible to be solved by any existing analytical Method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical Method based on the Atangana-Baleanu fractional derivative operator in the caputo sense. To believe upon the results obtained, the fractional order α has been allowed to vary between ( 0 , 1 ] , whereupon the physical observations match with those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional order derivatives for ABC. Finally, the fractional Forward Euler Method in the classical caputo sense has been used to illustrate the better performance of the numerical Method obtained via the Atangana-Baleanu fractional derivative operator in the caputo sense.In the present study, the fractional version with respect to the Atangana-Baleanu fractional derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its fractional version is not possible to be solved by any existing analytical Method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical Method based on the Atangana-Baleanu fractional derivative operator in the caputo sense. To believe upon the results obtained, the fractional...
Sergio Gómez - One of the best experts on this subject based on the ideXlab platform.
-
optimal stabilization and time step constraints for the Forward Euler local discontinuous galerkin Method applied to fractional diffusion equations
Journal of Computational Physics, 2019Co-Authors: Paul Castillo, Sergio GómezAbstract:Abstract A time dependent model problem with the Riesz or the Riemann-Liouville fractional differential operator of order 1 α 2 is considered. By penalyzing the primary variable of the minimal dissipation Local Discontinuous Galerkin (mdLDG) Method with a term of order h 1 − α and using a von Neumann analysis, stability conditions proportional to h α are derived for the Forward Euler Method and both fractional operators in one dimensional domains. The CFL condition is numerically studied with respect to the approximation degree and the stabilization parameter. Our analysis and computations carried out using explicit high order strong stability preserving Runge-Kutta schemes reveal that the proposed penalization term is suitable for high order approximations and explicit time advancing schemes when α is close to one. A series of numerical experiments in 1D and 2D problems are presented to validate our theoretical results and those not covered by the theory.
Erik Burman - One of the best experts on this subject based on the ideXlab platform.
-
error estimates for Forward Euler shock capturing finite element approximations of the one dimensional burgers equation
Mathematical Models and Methods in Applied Sciences, 2015Co-Authors: Erik BurmanAbstract:We propose an error analysis for a shock capturing finite element Method for the Burgers' equation using the duality theory due to Tadmor. The estimates use a one-sided Lipschitz stability (Lip+-stability) estimate on the discrete solution and are obtained in a weak norm, but thanks to a total variation a priori bound on the discrete solution and an interpolation inequality, error estimates in Lp-norms (1 ≤ p < ∞) are deduced. Both first-order artificial viscosity and a nonlinear shock capturing term that formally is of second order are considered. For the discretization in time we use the Forward Euler Method. In the numerical section we verify the convergence order of the nonlinear scheme using the Forward Euler Method and a second-order strong stability preserving Runge–Kutta Method. We also study the Lip+-stability property numerically and give some examples of when it holds strictly and when it is violated.
Baowei Yan - One of the best experts on this subject based on the ideXlab platform.
-
estimation of reservoir flood control operation risks with considering inflow forecasting errors
Stochastic Environmental Research and Risk Assessment, 2014Co-Authors: Shenglian Guo, Baowei Yan, Lu ChenAbstract:A Method for quantifying inflow forecasting errors and their impact on reservoir flood control operations is proposed. This approach requires the identification of the probability distributions and uncertainty transfer scheme for the inflow forecasting errors. Accordingly, the probability distributions of the errors are inferred through deducing the relationship between its standard deviation and the forecasting accuracy quantified by the Nash–Sutcliffe efficiency coefficient. The traditional deterministic flood routing process is treated as a diffusion stochastic process. The diffusion coefficient is related to the forecasting accuracy, through which the forecasting errors are indirectly related to the sources of reservoir operation risks. The associated risks are derived by solving the stochastic differential equation of reservoir flood routing via the Forward Euler Method. The Geheyan reservoir in China is selected as a case study. The hydrological forecasting model for this basin is established and verified. The flood control operation risks in the forecast-based pre-release operation mode for different forecasting accuracies are estimated by the proposed approach. Application results show that the proposed Method can provide a useful tool for reservoir operation risk estimation and management.