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Comparing numerical integration schemes for a car-following model with real-world data

Přikryl, Jan, Vaniš, Miroslav (2017)

Programs and Algorithms of Numerical Mathematics

A key element of microscopic traffic flow simulation is the so-called car-following model, describing the way in which a typical driver interacts with other vehicles on the road. This model is typically continuous and traffic micro-simulator updates its vehicle positions by a numerical integration scheme. While increasing the order of the scheme should lead to more accurate results, most micro-simulators employ the simplest Euler rule. In our contribution, inspired by [1], we will provide some additional...

Computing the differential of an unfolded contact diffeomorphism

Klaus Böhmer, Drahoslava Janovská, Vladimír Janovský (2003)

Applications of Mathematics

Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism Φ linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential D Φ ( 0 ) of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of D Φ ( 0 ) . Singularity classes containing bifurcation points with c o d i m ≤ 3 , c o r a n k = 1 are considered.

Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters

Anton Huťa, Karl Strehmel (1982)

Aplikace matematiky

In the article containing the algorithm of explicit generalized Runge-Kutta formulas of arbitrary order with rational parameters two problems occuring in the solution of ordinary differential equaitions are investigated, namely the determination of rational coefficients and the derivation of the adaptive Runge-Kutta method. By introducing suitable substitutions into the nonlinear system of condition equations one obtains a system of linear equations, which has rational roots. The introduction of...

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