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This image is a derivative work of the following images: Image:Composite_trapezoidal_rule_illustration_small.png licensed with PD-user-w 2007-09-22T13:48:59Z Glivi 2407x1603 (100944 Bytes) {{Information |Description=Composite trapezoidal rule illustration |Source=english wikipedia [[:Image:Composite_trapezoidal_rule_illustration_small.png ...
In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: (). The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area.
Another example for an implicit Runge–Kutta method is the trapezoidal rule. Its Butcher tableau is: The trapezoidal rule is a collocation method (as discussed in that article). All collocation methods are implicit Runge–Kutta methods, but not all implicit Runge–Kutta methods are collocation methods.
In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals. The trapezoidal rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multistep method.
The original can be viewed here: Composite trapezoidal rule illustration small.svg: . Modifications made by Jfer91 . This work is free software ; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation ; version 2.
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