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Assignment III
Ordinary Differential equations
- 1.
- Write a program to numerically integrate trajectories (using
the Euler method) for a
particle of unit mass moving in 1-D in the potenital
. Test the accuracy of your program for different step
sizes
by calculating the
energy along the trajectory. We expect the energy to be conserved.
Show the phase trajectory for
for the initial condition
,
at
for different step sizes.
- 2.
- Wite a program to numerically integrate the differential
equation
with the initial
condition
using the
Order Taylor Series
method. Use your program to integrate
to
using stepsizes
,
and
. Comment on how you expect the step
size to scale with
. Can you verify if this actually holds in your
results?
- 3.
- Write functions to solve differential equations with more
than one variables
using the
and
Order Runge-Kutta methods using fixed step size
. Use these functions to repeat the exercise in Question I of this
asignment sheet.
Somnath Bharadwaj
2002-01-16