THE PROBLEM OF INFORMATION STABILITY IN COMPUTER STUDIES OF CONTINUOUS SYSTEMS

The pervasive use of computers in scientific computation and simulatio n requires a paradigm shift in mathematical modelling from the continu ous mathematics that has dominated science since Newton to a mathemati cs that is simulateously both continuous and discrete. This will be il lustrated with examples from the research results of the authors and t heir coworkers, such as on Moire structures and the collapse of chaoti c dynamics under spatial discretization. Two basic questions are raise d and discussed. What kind of information about an underlying continuo us system is probably or inevitably lost in using a particular compute r representation? Can robustness of information be guaranteed in using discretization schemes?