Heun's method: Difference between revisions

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In [[mathematics]] and [[computational science]], '''Heun's method''' may refer to the '''improved'''<ref>{{Citation | last1=Süli | first1=Endre | last2=Mayers | first2=David | title=An Introduction to Numerical Analysis | publisher=[[Cambridge University Press]] | isbn=0-521-00794-1 | year=2003}}.</ref> or '''modified Euler's method''' (that is, the '''explicit trapezoidal rule'''<ref>

{{Citation | last1=Ascher | first1=Uri M. | last2=Petzold | first2=Linda R. | title=Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations | publisher=[[Society for Industrial and Applied Mathematics]] | ___location=Philadelphia | isbn=978-0-89871-412-8 | year=1998}}.</ref>), or a similar two-stage [[Runge–Kutta method]]. It is named after [[Karl L. W. M. Heun]] and is a [[numerical analysis|numerical]] procedure for solving [[ordinary differential equation]]s (ODEs) with a given [[Initial value problem|initial value]]. Both variants can be seen as extensions of the [[Euler method]] into two-stage second-order Runge–Kutta methods.

The procedure for calculating the numerical solution to the initial value problem via the improved Euler's method is: