Bisection Method, Interval Halving Method, Classical Algebra #39

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Angewandte Mathematik für Ingenieure

Published on Jun 8, 2024
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What is the bisection method or the interval halving method, and how can real equations with a real unknown be solved numerically, with in principle any degree of precision, using the bisection 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 bisection method. The bisection 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 bisection method successfully. Firstly, the function 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 bisection method is a very reliable numerical method that can be used to calculate the zeros of a real function with one unknown with any degree of precision. The algorithm of the bisection method essentially consists in continuously dividing the original closed initial interval into two (bisection), which then creates two new subintervals of half the length of the previous interval. The bisection method is therefore also known as the interval halving method or the interval nesting method. A concrete example task is used to show in detail how the bisection method can be used in practice. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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