BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:V. A. Gordin (National Research University "Higher School of Econo mics"\, Hydrometeorological Research Center of the Russian Federation\, Mo scow Institute of Physics and Technology\, Innopolis University) DTSTART:20260402T110000Z DTEND:20260402T120000Z DTSTAMP:20260423T024803Z UID:mmandim/109 DESCRIPTION:Title: The compact finite-difference scheme and modified Richardson extrapolati on for NLSE\nby V. A. Gordin (National Research University "Higher Sch ool of Economics"\, Hydrometeorological Research Center of the Russian Fed eration\, Moscow Institute of Physics and Technology\, Innopolis Universit y) as part of Mathematical models and integration methods\n\n\nAbstract\nA compact finite-difference scheme combined with predictor-corrector approa ch for solving quasilinear partial differential equations and systems is p resented. The nonlinear Schrödinger equation (NLSE) serves as a model pro blem to demonstrate the method’s capabilities. The proposed algorithm ac hieves fourth-order spatial accuracy and second-order temporal accuracy wh ile maintaining computational efficiency through linearization via Newton — Raphson iterations. As a rule\, one iteration is sufficient. The schem e was optimized according to the Courant parameter based on the criterion: the ratio of computational complexity to solution accuracy.\n\nAlso\, we introduce a modified two-dimensional and quasi-two-dimensional Richardson extrapolation technique that further enhances accuracy up to eighth-order. \n\nNumerical experiments confirm the scheme’s high precision and stabil ity across a range of Courant parameters as well as a good conservation of many first integrals of NLSE. The method is applicable to arbitrary smoot h initial data and various boundary conditions. We tested its properties o n various solutions (solitons\, collision of several solitons\, chains\, s hort-wave noise). In the latter two cases\, there is an alternation of cha otic and ordered types of solution behavior.\n\nThis is joint work with D. P. Milutin.\n LOCATION:https://researchseminars.org/talk/mmandim/109/ END:VEVENT END:VCALENDAR