=== Newton Numeric Example 1 === 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 [[ NewtonNumericExample1_Code | 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 | | |... | ... | ... | |