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Euler Forward Method


A method for solving ordinary differential equations using the formula

 y_(n+1)=y_n+hf(x_n,y_n),

which advances a solution from x_n to x_(n+1)=x_n+h. Note that the method increments a solution through an interval h while using derivative information from only the beginning of the interval. As a result, the step's error is O(h^2). This method is called simply "the Euler method" by Press et al. (1992), although it is actually the forward version of the analogous Euler backward method.

While Press et al. (1992) describe the method as neither very accurate nor very stable when compared to other methods using the same step size, the accuracy is actually not too bad and the stability turns out to be reasonable as long as the so-called Courant-Friedrichs-Lewy condition is fulfilled. This condition states that, given a space discretization, a time step bigger than some computable quantity should not be taken. In situations where this limitation is acceptable, Euler's forward method becomes quite attractive because of its simplicity of implementation.


See also

Courant-Friedrichs-Lewy Condition, Euler Backward Method, Newtonian Graph Explore this topic in the MathWorld classroom

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References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 710, 1992.

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Euler Forward Method

Cite this as:

Weisstein, Eric W. "Euler Forward Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerForwardMethod.html

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