The Regula Falsi Method, Classical Algebra #40

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Angewandte Mathematik für Ingenieure

Published on Jun 15, 2024
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What is the regular falsi method or the secant approximation method and how can real equations with a real unknown be solved numerically, with in principle any degree of accuracy, using the regular falsi method? In this video, physicist Dietmar Haase shows how the zeros of a real nonlinear function with a real variable can be found numerically using the regular falsi method. The regular falsi method is generally used to solve equations that cannot be solved algebraically or can only be solved with considerable computational effort. It is shown that two requirements must be met by the functions under consideration in order to be able to use the regular falsi method successfully. Firstly, the functions must be continuous on a closed real interval and furthermore, the function values ​​at the interval edges must have different signs. Under these two requirements, Bolzano's intermediate value theorem can then be applied, which guarantees that there must be at least one real zero of the function in the closed interval under consideration. The regular falsi method is a very reliable numerical method with which the zeros of a real function with one unknown can be calculated with, in principle, any degree of precision. The algorithm of the regular falsi method essentially consists in iteratively placing secants on the given real function, the zeros of which converge towards the desired zero of the function. The regular falsi method is therefore also called the secant approximation method. A concrete example task is used to show in detail how the regular falsi method can be used in practice. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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