A -stability of Runge-Kutta methods for systems with by Hernandez D. B., Spigler R.

By Hernandez D. B., Spigler R.

Numerical balance of either specific and implicit Runge-Kutta tools for fixing usual differential equations with an additive noise time period is studied. the idea that of numerical balance of deterministic schemes is prolonged to the stochastic case, and a stochastic analogue of Dahlquist's A-stability is proposed. it's proven that the discretization of the float time period on my own controls the A-stability of the complete scheme. The quantitative impact of implicitness upon A-stability can be investigated, and balance areas are given for a kin of implicit Runge-Kutta equipment with optimum order of convergence.

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Uiberacker^'^ R. Kienberger^'^ T. Fuji\ V. S. Yakovlev\ V. Smilgevicius^ R. Danielius^ A. Piskarskas^, and F. at ^ Max-Planck-Institut fur Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany ^ Laser Research Center, Vilnius University, Sauletekio ave. 10, LT-2040 Vilnius, Lithuania Abstract. We discuss routes towards developing an ultra-high peak power phase-stable source of few-cycle laser pulses suitable for driving a wide range of strong-field applications. 1-TW 5-fs system based on a Ti:sapphire amplifier and the progress in construction of a 1-TW few-cycle optical parametric amplifier are presented.

Second, the precise alignment of the 4 - / phase compensator was done. /•'"460 - 1060 nm (Av = 369 THz) (iii) ^-n 500 600 700 800 900 Wavelength [nm] jz p^ 1000 Fig. 2. Results of feedback phase compensation. (A) (i) Intensity spectrum. Spectral phases (ii) before, (iii) after 1st and (iv) after 2nd feedback chirp compensations. (B) detail of (iv). 14 spatially displaced position of the compensator output, by moving slightly b o t h distances of G2 and G l . Consequently, both positions of input 0 1 and output G2 gratings were adjusted to make the 4 - / configuration precisely dispersion-free.

Danielius^ A. Piskarskas^, and F. at ^ Max-Planck-Institut fur Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany ^ Laser Research Center, Vilnius University, Sauletekio ave. 10, LT-2040 Vilnius, Lithuania Abstract. We discuss routes towards developing an ultra-high peak power phase-stable source of few-cycle laser pulses suitable for driving a wide range of strong-field applications. 1-TW 5-fs system based on a Ti:sapphire amplifier and the progress in construction of a 1-TW few-cycle optical parametric amplifier are presented.

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