Computational Methods for Continuous Problems
CMCP_2013 is my home page for the class ISC4232-01/ISC5935-03,
"Computational methods for Continuous Problems", offered in Fall 2013,
by the Department of Scientific Computing at Florida State University.
The instructor for this course is Professor Janet Peterson. I have
been asked to assist in the course.
The primary information source for this course is
Professor Peterson's web page.
The course concentrates on the computational solution of differential
equations of the following kinds:
IVP, (initial value problems); the initial values of
one or more quantities are given, along with differential
equations that describe how these quantities change with time.
The task is to start with the initial values, and produce a table
of the values at subsequent times.
BVP, (boundary value problems); a physical region
is given, which might be a long iron bar, the surface of a drum,
or a block of metal. The value of some quantity (such as temperature)
is known on the outer boundary of the region, and a differential equation
is known which describes how this quantity is allowed to vary in the
interior. The task is to determine the values of the quantity in
IBVP, (initial boundary value problems); again,
a physical region is given, and a quantity is to be studied, whose
values on the exterior boundary are known. However, we now want to
follow the evolution of the interior values over time. To do this,
we must be given initial data (the value of the quantity everywhere
at the starting time) and boundary data (the value of the quantity
on the boundaries, for all time.) Moreover, the differential equation
becomes a partial differential equation, because it must describe
how the quantity changes over both time and space.
The task is to produce, at selected times, the value of the quantity
over a grid of points in the interior.
Lectures for the class are given Monday, Wednesday, and Friday
from 1:25pm to 2:15pm in room 152 DSL.
A weekly computer lab associated with the class is given Wednesday,
from 8:30am to 11:00am in room 152 DSL.
solves a two point boundary value problem with Gauss elimination.
solves a two point boundary value problem with Jacobi iteration.
uses Cholesky factorization to factor a (positive definite symmetric)
is an example of using Gauss elimination to solve a linear system.
takes single steps of a Jacobi iteration for a tiny linear system.
uses LU factorization (without pivoting) to factor a matrix.
a MATLAB program by Cleve Moler that illustrates the kind of
2D partial differential equations (steady heat, time dependent
heat, wave, eigenvalue) and various domains.
Some free texts are available.
Last revised on 30 September 2013.