Spring 2010
MAT260 – BEREGNINGSALGORITMER 2
Obligatory Exercise 2
Deadline: 29. April 15.00
Print your name and Candidate number on the front page, and
deliver your solutions to the problems below in a box marked
MAT260 in the ’Ekspedisjon’ office in the 5th floor
Problem 1
Use the Leapfrog method
a)
x
n
=
x
n
−
2
+ 2
hf
n
−
1
, n
= 2
,
3
, . . . ,
to integrate the differential equation
x
′
(
t
) =
x
(1

x
)
≡
f
(
t, x
)
,
four steps from
t
= 0 to
t
= 2 with initial value
x
(0) = 0
.
5. Use Euler’s
method in the first step. Write down the formulas you use to compute each
of the four
x
values.
The global error in the computed approximation of
x
(2) is of order two. Using
b)
eight steps from
t
= 0 to
t
= 2 gives
x
(2)
≈
0
.
88110. Use your own result
in combination with this result to estimate the error in the approximation
0
.
88110. Explain the assumptions that your error estimate is based on.
Write a Matlab function
[t,x] = Leap
frog(f,ts,te,xs,N)
which takes
c)
a total of
N
equidistant steps from time
t
=
ts
, with initial value
xs
, to
time
t
=
te
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 Spring '10
 Berntsen
 Linear Algebra, Orthogonal matrix, Gauss Quadrature Rule, Leapfrog method xn, Leapfrog method

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