QuoteOriginally posted by: AVtI do not mind ad hoc. There where fixed parameters, no?I agree to reject complex numerics for usual code. But use order=3 in E=0, 0 <= M < 1/3. Solving for the (first) real solution will do as guess, it should be X0 = rho/eps + 2*(eps-1)/rho where rho = ((3*M+(-12/eps^2*d)^(1/2))*eps^2)^(1/3), d= -1/12*eps*(9*M^2*eps-8*eps^3+24*eps^2-24*eps+8)Splitting at M=1/3 should let converge Newton in 3 - 5 steps. There is only 1 solution for 0 < eps < 1, as the function E-eps*sin(E)-M increases w.r.t. EI bet you did not spend Saturday evening working out this formulas by hand (place smile emoticon here) Did you generate it in Maple or something? And the rationale eludes me.This kind of approach only convinces me more that I don't like NR. I had something similar on a fixed-price fixed-income problem (I take on the project risk) to discover that the NR seed was word. As in this thread, I first bracket using Bisection method and then apply NR. It works really well. It's like interval arithmetic, the kind of stuff they put into the Apollo. ====When eps == 0 the seed explodes.
Last edited by Cuchulainn
on February 1st, 2015, 11:00 pm, edited 1 time in total.