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We propose to conduct research on contemporary numerical methods for wide classes of differential, integral and integro-differential equations arising in practice with main emphasis on establishing their fundamental properties like stability and convergence. In particular, the results of the planned research in this field should give a quite comprehensive description of the basic properties of main numerical methods for solving Volterra integro-differential equations and of the stability properties of B-wavelets, including the description of the dependence of the stability on the knot sequence. We plan to collaborate with scientists from other institutions and/or specialities in the investigation of several mathematical models arising in various applications. In addition to theoretical research of the models it is planned to conduct numerical experiments using data from actual measurements. In the field of mathematical models of economics, especially in mathematical finance, the proposed research includes establishing connections between discrete an continuous models, investigation of various ways of defining and measuring economical risks and establishing new methods for describing the term structure of interest rates. |