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Solving Backward Euler with Newton's Method

  1. Dec 3, 2009 #1
    Greetings, I am trying to implement backward euler implicit method by newton-raphson iteration. The differential equation is for a simple planar pendulum. So the function for the pendulum is :

    (1) angularAcceleration (angle) = ( -gravity/length ) * sin(angle);

    and the update function for implicit integration is:

    (2) u_(t+1) = u_t + deltaTime * velocity_(t+1)

    velocity_(t+1) = velocity_t + deltaTime * angularAcceleration ( u_(t+1) )

    My question is: given that newton's method is stated as x_(i+1) = x_i - f( x_i) / f ' (x_i) ,
    what is the f in newton's method? Is it the residual of the pendulum function given by (1) or the residual of the update step given by (2)?

    Thanks in advance!
  2. jcsd
  3. Dec 3, 2009 #2
    Need to be clear about the notation first.

    Is your u_ the approximation for angle ?

    Is your velocity_ the approximation for angularVelocity (angle) ?
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