Beeman's algorithm

<p>Beeman's algorithm is a method for <a href="/facts/Numerical_quadrature/MwJnvcDV">numerically integrating</a> <a href="/facts/Ordinary_differential_equation/ygKGQ8kD">ordinary differential equations</a> of order 2, more specifically Newton's equations of motion 
  
    
      
        
          
            
              x
              ¨
            
          
        
        =
        A
        (
        x
        )
      
    
    {\displaystyle {\ddot {x}}=A(x)}
  
. It was designed to allow high numbers of particles in simulations of molecular dynamics. There is a direct or explicit and an implicit variant of the method. The direct variant was published by Schofield in 1973 as a personal communication from Beeman.  This is what is commonly known as Beeman's method. It is a variant of the <a href="/facts/Verlet_integration/Wtzt8hkX">Verlet integration</a> method.  It produces identical positions, but uses a different formula for the velocities. Beeman in 1976 published a class of implicit (predictor–corrector) multi-step methods, where Beeman's method is the direct variant of the third-order method in this class.
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Beeman's algorithm open-in-new

Beeman's algorithm