1. ME 123 Computer Applications I Lecture 23: Advanced Graphics 4/17/03

2. ME 123 Computer Applications I
Hint on Project
Dan asked an excellent question on error estimation on Tuesday. Since it is useful to your project, I would like to reiterate on the idea.
Assume you have two time-marched solutions obtained with different step size (yN,Dx and yN,Dx/2) and want to estimate the error in each one of them. What should you do?
If they are obtained by the fourth-order Runge-Kutta method, the errors in the two solutions are expected to be:
Since the exact solution and the value of C are both unknowns, the two equations need to be solved to obtain the two unknowns.
A simple subtraction reveals that the error in the large step size solution is
Lecture 23
ME 123 Computer Applications I

3. Hint on Project (cont’d)
The line of reasoning can be applied to time marching method of different order of accuracy. In the literature, it is called the Richardson extrapolation for error estimation.
If the time marching method is the Explicit Euler method, what will the result be?
As you have more questions on the project, I will address them accordingly.
I would be excited to see more of excellent questions like this one!
Lecture 23
ME 123 Computer Applications I

4. ME 123 Computer Applications I
Road Map of Lecture 23
Solutions to HW 6-2
Graphical display and interpretation of complex data sets
Multiple plots on a single page
3D plots
Contour plots
Vector plots
Streamlines/flux lines
Graphical means to problem solving in multi-dimensions
solution search as an example
Lecture 23
ME 123 Computer Applications I