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Expanding the applicability of two-point Newton-like methods under generalized conditions

Ioannis K. Argyros, Saïd Hilout (2013)

Applicationes Mathematicae

We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied....

Experimental comparison of traffic flow models on traffic data

Horňák, Ivan, Přikryl, Jan (2015)

Programs and Algorithms of Numerical Mathematics

Despite their deficiencies, continuous second-order traffic flow models are still commonly used to derive discrete-time models that help traffic engineers to model and predict traffic oflow behaviour on highways. We brie fly overview the development of traffic flow theory based on continuous flow-density models of Lighthill-Whitham-Richards (LWR) type, that lead to the second-order model of Aw-Rascle. We will then concentrate on widely-adopted discrete approximation to the LWR model by Daganzo's...

Experiments with Krylov subspace methods on a massively parallel computer

Martin Hanke, Marlis Hochbruck, Wilhelm Niethammer (1993)

Applications of Mathematics

In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total...

Explicit conjugate gradient method with preconditioning

Jitka Křížková, Petr Vaněk (1994)

Applications of Mathematics

An algorithm of the preconditioned conjugate gradient method in which the solution of an auxiliary system is replaced with multiplication by the matrix M = I - ω A for suitably chosen ω is presented.

Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis

A. Poliński (2006)

Annales Polonici Mathematici

We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.

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