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Differential
Equations (92.236)
Listing of Matlab Demos
This
page contains a summary list of the Matlab demos available for this
course. The list is organized roughly by subject and by the order
that the files are discussed. These files will be used in the Matlab
lab sessions and they can also be used as a guide for many of the
Matlab assignments given throughout the semester. Quite often, only
minor modifications to these demos are needed to solve similar HW
problems. Careful study of these sample problems should make the
Matlab assignments quite straightforward and also give you a solid
understanding of various problem solving strategies and techniques
within Matlab.
You can view a particular Matlab file or download it by simply clicking
the right mouse button
on the link over the file name. From here you can either choose
"open in new window" to view the file online or "save
target as" to download the file directly to your PC (note that
these commands might differ slightly depending on your choice of
web browser). In any case, once the file is on your machine, you
can run it just like any other Matlab script file. Good Luck and
enjoy!!!
Introduction
to Matlab
Introduction to some basic Matlab plotting capabilities and
syntax. 

Evaluate
and plot analytical expressions in a number of different ways.
This file is a good starting point for the plots requested as
part of HW #2. 

Evaluate
and plot analytical solutions to a particular IVP treated in
class. 

Evaluate
and plot multiple curves on a single axis. This Matlab file
gives an example that produces plots that are very similar to
the curves requested as part of one of the problems for HW#5. 

This
demo represents a collection of short examples that illustrate
several Matlab programming features and general tips. It is
used as part of one of the Matlab lab sessions. 

These
two files are needed for one of the Matlab lab sessions. They
will be used to illustrate various analysis and plotting techniques
for 2nd order systems. 
Slope
Fields
Capability and illustrations for generating slope fields. 

A
Matlab function file that plots a slope field for a 1st order
ODE (uses Matlab's quiver function). 

Plot
slope field and solution curves for demonstration problem from
the text. These files require function file sfield.m. 

This
is similar to SF_DEMO1 but it only plots the slope field (no
solution curves). This demo is a good starting point for the
Matlab plots requested as part of HW #4. These files require
function file sfield.m. 

These
three separate demos plot the slope field and solution curves
for three different first order systems. They simply provide
additional examples similar to the SF_DEMO1 and SF_DEMO2 sequence.
These files also require the sfield.m function.

Numerical
Methods
Capability and demos for numerical solution of IVPs.


Function
files to implement different numerical solution schemes for
first order ODEs. These files implement the Euler, Improved
Euler, and 4th Order Runge Kutta Methods, respectively. These
function files must be called from a main program. 

Sample
program to illustrate the Euler Method. The example differential
equation is contained in function file eqn1.m. 

Sample
program to illustrate the Improved Euler Method. The example
differential equation is contained in function file eqn1.m. 

Sample program to illustrate the 4th Order Runge Kutta Method
(RK4 Method). The example differential equation is contained
in function file eqn1.m. 

Sample
program to illustrate four different numerical solution techniques
including the Euler, Improved Euler, and RK4 Methods as well
as Matlab's builtin ode23 function. ode23 uses an adaptive
step control method so that, instead of the step size, one specifies
the desired tolerance for the problem. The example differential
equation is contained in function file eqn1.m. 

Interactive
Numerical solution of ODEs. This Mfile solves an IVP using
one of four numerical integration schemes  Euler, Improved
Euler, 4th Order RK, or the adaptive predictorcorrector method
within Matlab. The function file containing the definition of
f(x,y) is selected interactively or the user can type in the
function f(x,y). The second option calls a generic function
file, sfode.m, which evaluates the function f(x,y) input via
the keyboard. 

Numerical
Solution of ODEs using a variety of methods. This Mfile solves
the given IVP using a full selection of numerical integration
schemes  Euler, Improved Euler, 4th Order RK, and the adaptive
predictorcorrector method within Matlab. The solution vectors
are plotted together to demonstrate the accuracy obtained with
the different methods. The function file containing the function
definition is selected interactively. 

Plot
solution for P(t) for HW9_DEMO1. This example uses Matlab's
ode23 routine to solve a simple population model. 

Plot
solution for x(t) and v(t) for HW9_DEMO3. This example uses
Matlab's ode23 routine with two ODEs with two dependent variables,
x(t) and y(t). It uses a simple vector notation. This is our
first example of a system of ODEs. 
Some
Applications
Demos with numerical applications requiring two equations.


Generates
solution curves for HW14_DEMO1. These files use Matlab's builtin
ODE solver to numerically integrate a system of two firstorder
ODEs. Comparison to the analytical solution is given. The symbolic
solution using Matlab's dsolve command is also
generated. 

Generates
solution curves for HW14_DEMO2. These files use Matlab's builtin
ODE solver to numerically integrate a system of two firstorder
ODEs. Comparison to the analytical solution is given. The symbolic
solution using Matlab's dsolve command is also
generated. 
Laplace
Transforms
Demos for taking Laplace and inverse Laplace transforms.


Demo
which illustrates how to take Laplace transforms using the Matlab
function LAPLACE from the Symbolic Toolbox. 

Demo
which illustrates how to take inverse Laplace transforms using
the Matlab function ILAPLACE from the Symbolic Toolbox. 
Additional
detailed modeling and simulation applications are also available
for First Order Systems and
for Second Order Linear and Nonlinear Systems.
These cases focus on the development and solution of the resultant
differential equations. They offer, in some cases, significant additional
insight into the problem formulation and systematic arguments that
lead to the desired solution. Some of these applications also offer
additional Matlab implementations and the links to these applicationoriented
Matlab files are given in the following tables:
Applications
involving First Order Systems
Demos from the Lecture Notes on First Order Systems.


Matlab
file for the Bombs Away application.


Matlab
files for the Two Salty Tanks application. 

Matlab
files for the application, A Fish Story. 
Last
updated by Prof. John R. White (Feb. 2007)
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