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Simulation of analog computer in solving nonlinear differential equations by a digital computer. (English) Zbl 0598.65048

This paper is concerned with nonlinear function generators for the use on analog computers. Only piecewise linear approximations for a real single variable function f on a finite interval [a,b] are discussed. The author proposes following versions of approximation: piecewise linear interpolation with uniformly distributed knots; piecewise linear interpolation with a special choice of knots in order to get equal supremum error on each subinterval; piecewise linear approximation with the additional condition that the integral divided by (b-a) of the original function and its approximating spline should be equal. Flow diagrams of programs for digital computer and some numerical results for \(f(x)=x^ 2\), \(x^ 3\), \(\sqrt{x}\) are given.
Reviewer: K.Moszyński

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65D15 Algorithms for approximation of functions
68U20 Simulation (MSC2010)
34A34 Nonlinear ordinary differential equations and systems
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