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Rombergs Method of Numerical Integration and its Implementation in MATLAB
A method suggested by Romberg in 1955 is shown to be a very efficient, accurate and fast. In this paper an implementation of the Romberg method in MATLAB is discussed and illustrated using example. Two modifications of the method are provided, one based on the use of the trapezoidal rule, and another one using the Simpson rule. The paper starts with an overview of some most basic approaches to the numerical integration. The place of the Romberg method in the classification of classical approaches is shown, and linked to Richardsons extrapolation method, which is used for the acceleration of convergence of numerical methods. The results of implementation are demonstrated in the form of comparison tables. It is demonstrated that the Romberg method gives a high precision for the price of the good time performance, and therefore represents a competitive alternative to MATLABs standard functions for numerical integration.
Rombergs Method of Numerical Integration and its Implementation in MATLAB
A method suggested by Romberg in 1955 is shown to be a very efficient, accurate and fast. In this paper an implementation of the Romberg method in MATLAB is discussed and illustrated using example. Two modifications of the method are provided, one based on the use of the trapezoidal rule, and another one using the Simpson rule. The paper starts with an overview of some most basic approaches to the numerical integration. The place of the Romberg method in the classification of classical approaches is shown, and linked to Richardsons extrapolation method, which is used for the acceleration of convergence of numerical methods. The results of implementation are demonstrated in the form of comparison tables. It is demonstrated that the Romberg method gives a high precision for the price of the good time performance, and therefore represents a competitive alternative to MATLABs standard functions for numerical integration.
Rombergs Method of Numerical Integration and its Implementation in MATLAB
Kačeňák Martin (Autor:in)
2001
Aufsatz (Zeitschrift)
Elektronische Ressource
Unbekannt
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