- #1
jacki
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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!
(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!