Solving ordinary differential equation systems by approximation in a graphical way.

Geda, Gábor; Vágner, Anikó

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A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^{3}$ . We investigate some of it’s properties, and begin the study of non-convex cases.

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This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves $Γ (t) : S \to ℝ^{2}$ , $t ≧ 0$ . The curves are driven by the normal velocity $v$ which is the function of curvature $κ$ and the position. The evolution law reads as: $v = - κ + F$ . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability...

Regularization parameter selection in discrete ill-posed problems - the use of the U-curve

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To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called...