Computational Project #1

y0 = 􀀀2xy 1; y(0) = 0 (1)
(b) Use Octave to plot the slope elds and the particular solution of equation(1). For the plot use
a window size of xmin = 􀀀1, xmax = 3, ymin = 􀀀1, ymax = 3.
(c) Use Octave to numerically solve (1) using n = 100 and n = 200 points. Create a plot showing the
two numerical solutions and the analytic solution from part(a). For the plot use xmin = 0, xmax = 8.
(d) Type a report using the following outline as a guide:
ˆ I. Introduction and Objectives
ˆ II. Discussion of the Euler’s Method
ˆ III. Discussion of Implementation
{ How were the methods implemented?
{ What kind of problems did you encounter while working with the code?
{ How did you overcome these problems?
ˆ IV. Discussion of Results
{ e.g. compare Euler’s solution with the analytical solution
ˆ V. Summary and Conclusion
Use MLA format for paper and provide references when necessary.
Items to Submit (three items):
octave file for the slope fields (.m file)
octave file for the Euler approximation (.m file)
pdf file of your typed paper (.pdf file)