Abstract
Abstract The pervasive use of computers in scientific computation and simulation requires a paradigm shift in mathematical modelling from the continuous mathematics that has dominated science since Newton to a mathematics that is simulateously both continuous and discrete. This will be illustrated with examples from the research results of the authors and their coworkers, such as on Moire structures and the collapse of chaotic dynamics under spatial discretization. Two basic questions are raised and discussed. What kind of information about an underlying continuous system is probably or inevitably lost in using a particular computer representation? Can robustness of information be guaranteed in using discretization schemes?
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