Time integration error estimation for continuous Galerkin schemes

Comparing Numerical Integration Schemes for Time-Continuous Car-Following Models

When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the forth-order Runge-Kutta method (RK4) are rarely used while the simple Euler’s method is popular among researchers. We compare four explicit methods: Euler’s method, ballistic update, Heun’s method (trapezoidal rule), and the standard forth-order RK4. As performance metrics,...

Error estimation of ‎f‎uzzy Newton-Cotes method for Integration of fuzzy functions‎

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

Comparison of two integration schemes for a micropolar plasticity model

Micropolar plasticity provides the capability to carry out post-failure simulations of geo-structures due to microstructural considerations and embedded length scale in its formulation. An essential part of the numerical implementation of a micropolar plasticity model is the integration of the rate constitutive equations. Efficiency and robustness of the implementation hinge on the type of int...

Nonlinear bounded-error state estimation of continuous-time systems

Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems

We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree p and p +...