Numerical Solutions Applied To Heat Transfer And
Use of Numerical Methods
During your education you've been taught a large number
of clever tricks to solve various mathmatical equations (algebraic,
ODE, PDE). However, as you look carefully at the mathmatical
models for problems of serious interest, you find that they are too
complex for any of these tricks to get you far in obtaining a solution
to the problem. In the end you find that you need to construct
approximations to the mathmatical model and solve these approximations
on a computer. This class with provide the basics for
constructing and evaluating such approximations. In the process
it will hopefully help you refine your skills in breaking a complex
problem into a series of relatively simple steps.
What is the basic approach?
Physical phenomena are defined by a mathematical
The mathematical model is approximated by algebraic
at discreet points or volumes in the physical domain.
The set of algebraic equations are solved
using the digital computer.
Use commercial program.
Use public domain ("freeware") program
Write your own program.
Has adequate detail been included in the
If the set of algebraic equations are solved
using an iterative method, have you obtained a converged system?
Is the measure of convergence adequate?
Is the solution independent of the number of
Created by Frank Schmidt
Maintained by John