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A numerical method intended for the search of steady state regimes of a system with servo. (Russian. English summary) Zbl 0786.34018

Filippov, S. S. (ed.), Numerical solution of ordinary differential equations. Collection of scientific works. Moskva: Institut Prikladnoj Matematiki Im. M. V. Keldysha AN SSSR, 139-147 (1988).
A method is proposed for numerical integration of stiff ordinary differential equations having a peculiar form \[ \dot x(t)= X(x,y),\quad \varepsilon\dot y(t)= Y(x,y),\tag{1} \] emerging in study of the dynamics of mechanical devices with servo. Here \(x\) and \(X\in\mathbb{R}^ m\), \(y\) and \(Y\in\mathbb{R}^ n\), and \(\varepsilon>0\) is a small scalar parameter. The essence of the method is as follows: the equations of the device motion and those of the servo are integrated simultaneously using different numerical methods with different temporary step sizes.
For the entire collection see [Zbl 0776.00006].

MSC:

65J99 Numerical analysis in abstract spaces
34E13 Multiple scale methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65-04 Software, source code, etc. for problems pertaining to numerical analysis
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