Marat S. Mukhametzhanov

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where the function f(x, y) in (1) has an unknown for the user analytical representation, i.e., is a “Black-box” function, very often can be found in practice. In the literature, there exist numerous numerical methods proposed to solve (1) (see, e.g., [1,2,5,6,10]). Usually, the accuracy of methods depends on the value of the integration step h. Since(More)
New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the(More)
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