(4) Consider the equation dz(t) =(205+0.1), with initial condition z(0) = 1.0. Find an approximate solution to z(1) by evolving the system from t=0 tot = 1 with a single 2nd-order Runge-Kutta step. Give a rough quantitative estimate of the discretisation error by comparing two different methods or two different step sizes.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(4) Consider the equation
dr(t)
dt
=(205+0.1)et,
with initial condition z(0) = 1.0. Find an approximate solution to (1) by evolving the system
from t = 0 tot = 1 with a single 2nd-order Runge-Kutta step. Give a rough quantitative estimate
of the discretisation error by comparing two different methods or two different step sizes.
=
Transcribed Image Text:(4) Consider the equation dr(t) dt =(205+0.1)et, with initial condition z(0) = 1.0. Find an approximate solution to (1) by evolving the system from t = 0 tot = 1 with a single 2nd-order Runge-Kutta step. Give a rough quantitative estimate of the discretisation error by comparing two different methods or two different step sizes. =
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