Assignment 6 AMATH 740, CS 770, CM 750


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C. Moler ”Numerical Computing with Matlab” (online, free download), Ch. 7
1. Show that no choice of coefficients in the one parameter family of the explicit two stage
Runge-Kutta methods derived in class will result in the local error of order 4.
2. Consider the following method
yn = yn−1 + h(θf(yn) + (1 − θ)f(yn−1)), 0 ≤ θ ≤ 1,
for solution of y
0 = f(y).
(a) Compute the local error dn. For what value of θ, dn is the smallest? Why does this
(b) Find the values of θ for which the absolute stability region contains the whole left half
plane of the complex plane?
3. Exercise 7.5 in Moler. It is not necessary to strictly follow the format of ode23tx. Note that
Octave does not have ode113, so you do not have to consider it.