Unformatted text preview: d. You may use the classical, Fehlberg, Dormand and
Prince, or other formula as long as it is fourth order.
55 1.2. Test your procedure using xed step integration with step sizes h = 1/2, 1/4,
1/8, : : : using the test IVPs y =y
0 and y(0) = 1 0 1 d2y + 2k dy + n2 y = 0
y(0) = 1
dyoverdt(0) = 0: For the second example use n = 10, k = 6 and n = 10, k = 8. In each
case, present results (tables and/or graphs) of the global error and number of
function evaluations as functions of h. Estimate the rate of convergence of the
method and compare it with the theoretical rate.
1.3. Replace the xed step size strategy above with a variable step size technique of
your choice. Base step size selection on control of the local error, which may be
estimated using either step doubling or embedding. Compare the performance
of your code on the above problems with the xed step performance. 56 Bibliography
1] M. Abromowitz and I. Stegun. Handbook of Mathematical Functions. Dover, New
2] R. Alexander. Diagonally implicit runge-kutta meth...
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- Spring '14
- Numerical Analysis, yn, Tn, Numerical ordinary differential equations