Fuchs: Modeling of Uniform Dynamical Systems  —  Chapter 5
CHAPTER 5: Numerical Methods for Differential Equations


In this chapter we will discuss a few of the many numerical methods which can be used to solve initial value problems and one-dimensional boundary value problems. Today, users would only rarely develop or program algorithms themselves. Nonetheless, one must know what the algorithms and properties of various groups of methods are.
There are two groups of methods, namely single-step or multi-step methods. These are again divided into the sub-groups of explicit or implicit methods. The simplest of these will be mentioned here. One of their most important properties, their stability, will be investigated in an exemplary manner. The same will be done with the problem of numerical accuracy.


Practical Problems With Numerical Solutions 166
Stability and Accuracy of Numerical Solutions 170
Stiff Differential Equations 178
Some Examples of Numerical Methods 181
Error Estimation and Automatic Step Control 189
Finite Element Methods for One Dimensional Boundary Value Problems 191

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