9478

Graphic Solution of a First-Order Differential Equation

This Demonstration presents Euler's method for the approximate (or graphics) solution of a first-order differential equation with initial condition , .
The method consists of calculating the approximation of by
,
,
where .
These coordinates determine points , , …, . These points form Euler's polygonal line that is an approximate solution of the problem. The Demonstration compares it with a better solution provided by Mathematica's built-in NDSolve function (brown line).

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Reference
[1] L. Euler, "De Integratione Aequationum Differentialium Per Approximationem," Institutionum Calculi Integralis Volumen Primum, 1768. www.math.dartmouth.edu/~euler/docs/originals/E342sec2ch7.pdf.
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