Transcription of Numerical Methods for Differential Equations
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Numerical Methods for Differential Equations
1. Numerical Methods for Differential Equations 1. 2 Numerical Methods FOR Differential Equations . Introduction Differential Equations can describe nearly all systems undergoing change. They are ubiquitous is science and engineering as well as economics, social science, biology, business, health care, etc. Many mathematicians have studied the nature of these Equations for hundreds of years and there are many well-developed solution techniques. Often, systems described by Differential Equations are so complex, or the systems that they describe are so large, that a purely analytical solution to the Equations is not tractable. It is in these complex systems where computer simulations and Numerical Methods are useful.
The fundamental concepts in this chapter will be introduced along with practical implementation programs. In this chapter we will present the programs written in the MATLAB programming language. It should be stressed that the results are not particular to MATLAB; all the programs in this chapter could easily be implemented in
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