Research and Development of Numerical Analysis Software

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Methods for numerical solution of initial value problem for systems of stiff ordinary differential equations are studied. Existence of 5-stage singley diagonally implicit one-step methods of order 5 is proved. Starters for numerical solution methods are obtained for a singular systems of differential equations of the second order. It has been shown that there exist two-step methods of order 4, 5 and 6 which enable us to estimate the local error and to interpolate at nonstep points and that there exist such methods with one off-step point of order 5, 6 and 7.The behavior of solution curves of nonlinear systems in the neighborhood of a nonsimple bifurcation point is studied in detail. Methods for constructing extended systems to determine double and triple turning points are developed.Characterization of semi-regular and regular experimental designs is given and nonexistence of a certain kind of design is proved.A personal computer program is written for diagnosing the ability of adding two integers of two figures.