Semi-implicit Euler method: Difference between revisions

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Note the difference from the Euler method: <math>x_{n+1}</math> depends on <math>v_{n+1}</math> rather than <math>v_n</math>.
 
== Example ==
 
For a spring undergoing [[simple harmonic motion]] we have the following
 
:<math>F = -kx = ma \quad</math>
 
:<math>\Rightarrow a = -{k \over m}x \quad</math>
 
Thus we have solutions
 
:<math>v_{n+1} = v_n - {k \over m}x_n\Delta t \quad</math>
 
:<math>x_{n+1} = x_n + v_{n+1} \Delta t \quad</math>
 
== See also ===