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Picard's Method of Successive Approximations Calculator

Auteur :Greg Petrics

Instructions:

To use this calculator:
  1. Enter a differential equation in the box for "dy/dx"
  2. Enter an initial value for . In other words enter the value of . Note: This calculator only works for initial values when ; sorry!
  3. Slide for the desired number of successive approximations. Note: the approximation very likely goes off the screen for larger values of ; click and drag the left pane to view more terms of the approximation if needed.
Note: The specific solution is also plotted for many simple differential equations, that said it's easy to break the automated solver; if so the page will timeout and ask you to reload it. Also Note: If the integrals of the Picard Sequence become overly complex, it is possible that you will not get higher order approximations due to a timeout. It's not that the Picard Sequence doesn't exist, it's just that GeoGebra can't calculate it, and in cases like this, the Picard Sequence is only of theoretical importance, not practical importance. This is frequently seen in differential equations with rational expressions with in the denominator.

A Few Suggestions

  1. dy/dx = (3x^2 - x^4) * y and y_0 = 1 is cool to see some insight into how the method works
  2. dy/dx = 3x^2 and y_0 = 1 is cool to see what happens in the case of a very simple differential equation (that's really just a Calc 1 integral)
  3. dy/dx = sin(x)*y and y_0 = 1 to see the impact of trigonometric functions.

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