Computational Project # 4
Due April 11
Write a program to solve
() ()
1tanh
2
dy
x
yx
dx =−
(
)
01,0 30yx
=
≤≤
using the following schemes:
i) Explicit Euler,
ii) Implicit Euler,
iii) Trapezoidal Method,
iv) Second order Runge-Kutta.
Do not use any build-in Matlab time integration routines. Try values 1, 3.5, 4.25x
Δ
=.
Plot the exact solution
()
()
cosh
1
x
yx= and the results of numerical integration for
different values
x
Δ for four different integration methods in separate sub-windows.
Explain the results in terms of stability and accuracy.
P.S. Bring your solution to class. Email your code to [email protected]. The
program that you send should be a working program. All the codes will be checked
whether they run or not. If they are erroneous, but run, points will be taken for the errors.
If the code does not run (it has some syntax errors), an additional 25% will be taken off.
The goal of this class is for you to be comfortable solving engineering problems. Please
take your time and learn how to trust the computer.