Abstract
Numerical integration (quadrature) of proper integrals is characterized by a big variety of methods. This chapter discusses the rectangular rules (based on the forward, backward, and central difference approximation), the trapezoidal rule, and the Simpson rule as a multi-point integration method. It moves on to a more general description - the Newton - Cotes rules and, in particular, to the Romberg method. The Gauss - Legendre quadrature is introduced as a very efficient alternative. Finally, the treatment of improper integrals and of multiple integrals is discussed. Particular emphasis is on the errors involved.
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Notes
- 1.
Particular care is required when dealing with periodic functions!
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Stickler, B.A., Schachinger, E. (2014). Numerical Integration. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-02435-6_3
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DOI: https://doi.org/10.1007/978-3-319-02435-6_3
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