Molodetska K. Improving the accuracy of modeling of physical processes and fields based on algebraic properties of differential spectra

Dissertation is sanctified to the decision of actual scientific task of increase of exactness and efficiency of symbol mathematical descriptions of physical processes and fields of objects of new technique and new technologies of their exploitation in the different modes of functioning. The method of design of physical processes and fields is first worked out, that differs from the properties of algebra of differential spectrums known for application, that allows to bring down an estimation from above absolute error of design at 2q one times, where q is a number of last taken into account discretes. The method of design of physical processes and fields purchased further development, that differs from known plugging in balance of differential spectrums of initial and maximum conditions in such form that allows regularizate an ill-conditioned problem. The method of design of physical processes, that differs from the known decisions of ill-conditioned problem application the systems of unidimensional differential transformations, that in area of images provide the interface of differential spectrums, that allows to decrease calculable complication is improved. Methodology of design of physical processes and fields is first worked out on the basis of properties of algebra of differential spectrums, that differs from known the diminished size of top limit of error, that allows to design physical processes and fields on the extended intervals.