Let us consider simple 1-node circuit

--------+------------- | | | I=0.001 R=1000 i=V^3/1000 | | | --- --- ---

Which is equivalent to equation:

F(V) = I + V/R + N(V) = V/1000 + 1/1000*V^3 - 0.001

J(V) = 1/1000 + 3/1000 * V^2

F'(V)= 3/1000*V^2*V + 0.001 - 1/1000*V^3

model code and circuit file for this example are here

Iteration sequence for this equation will be:

Iteration | Newton classic (2,3) | Gnucap's Newton Modification (5,6,7) | Damped |
---|---|---|---|

0 | V0=0 | V0=0 | |

J=0.001 | J=0.001 | ||

F=-0.001 | F' = 0.001 | ||

S=F/J=-1 | R =F'/J=0.001/0.001=1; | ||

V1= V0-S = 1 | V1 = R = 1 | ||

1 | V1=1 | V1 =1 | |

J=0.004 | J = 0.004 | ||

F=0.001 | F' =0.003 | ||

S=F/J=0.25 | R=F'/J=0.75 | ||

V2=V1-S=0.75 | V2=R=0.75 | ||

2 | V2=0.75 | V2=0.75 | |

J=0.0026875 | J=0.0026875 | ||

F=0.000171875 | F'=0.00184375 | ||

S=F/J=0.063953 | R=F'/J=0.686047 | ||

V3=V2-S=0.0686047 | V3=R=0.686047 | ||

3 | V3=0.0686047 | V3=0.0686047 | … |

J=0.0024119815 | J=0.0024119815 | ||

F=0.00000894221 | F'=0.00164579043 | ||

S=F/J=0.003707 | R=F'/J=0.68234 | ||

V4=V3-S=068234 | V4=R=0.68234 | ||

… | … | … |