Solution Verifier 2D
If you have a formulas which express the solution of a system of equations
dx/dt = f(x, y, t)
dy/dt = g(x, y, t)
in terms of the initial condition x=x0, y=y0 at t=t0:
x = A(x0, y0, t0, t)
y = B(x0, y0, t0, t)
then you can plug it in the applet and see if blue curves (numerical
solutions) coincide with red curves (obtained from your formula). You
can also use this method to verify whether your formula holds for some
particular initial conditions.
In the example below, we compare the solution to the equation
d^2x/dt^2 = t + x - x^2 to its Taylor series solution. First, this
equation is re-written as a system of two equations:
dx/dt = y
dy/dt = t + x - x^2
and the resulting system is fed into the applet.
View
Instructions on using the Applet
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unframed version
Marek Rychlik (rychlik@u.arizona.edu)
Author's Home Page: http://alamos.math.arizona.edu
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