Open AccessTHE STABILITY CONDITIONS OF FINITE DIFFERENCE SCHEMES FOR SCHRÖDINGER, KURAMOTO‐TSZUKI AND HEAT EQUATIONS
Author(s) -
Mindaugas Radziunas,
Feliksas Ivanauskas
Publication year - 1998
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.1998.9637101
Subject(s) - mathematics , boundary value problem , stability (learning theory) , initial value problem , finite difference method , heat equation , finite difference , norm (philosophy) , mathematical analysis , periodic boundary conditions , kuramoto model , combinatorics , topology (electrical circuits) , synchronization (alternating current) , computer science , machine learning , political science , law
We consider various finite difference schemes for the first and the second initial‐boundary value problems for linear Kuramoto‐Tsuzuki, heat and Schrödinger equations in d‐dimensional case. Using spectral methods, we find the conditions of stability on initial data in the L2 norm.