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5

This is just a starting point, which obviously needs some tests for convergence etc. f[x_] = x^3 - x - 1 NestWhile[# - f[#]/f'[#] &, 1, Abs[f[#]] > 10^-7 &]


0

for example for function y'=f(x,y)=x-y , I think the easiest way is... f[x_, y_] := x - y yn[x_,n_,x0_,y0_]:=If[n>0, y0+Integrate[f[s,yn[s,n-1,x0,y0]],{s,x0,x}], y0] example (y(0)=1 and 3 iterations): yn[x, 3, 0, 1] 1 - x + x^2 - x^3/3 + x^4/24



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