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.
0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 time y y=e−t Euler [t 0,y 0] [t 1,y 1] [t 2,y 2] [t 3,y 3] [t 4,y 4] Fig. 1.3 Graphical output from running program 1 in MATLAB. The points connected by the dashed line are the results of the numerical solution and the solid line is the exact solution. The time step size is. This large time step size results in
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