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 :(adsbygoogle = window.adsbygoogle || []).push({});

(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!

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# Solving Backward Euler with Newton's Method

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