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After read Michael answer, code use NestList to compute and feed in numerical integration. I want to learn this idea into my code.

In the NestList document, this function have three parameter, eg. f, expr, n.if define f, NestList seems to map expr to f[expr],'f[f[expr]]',... n times.

So I refer Michael code,

deltat = 1*^-3;
integrator[x_, y_, {x0_, y0_}] := {x[1], y[1]} /. 
   FindRoot[{x[1] - x[0] == deltat,
      y[1] - y[0] == deltat}, {{x[0], x0}, {y[0], y0}}];
integrator[x, y, {0, 0}]

And

NestList[integrator[x, y, {y[0], y[0]}], {x[0], y[0]}(* condition *), 4]

I want calculate 4 times nesting, at beginning, $x0,y0$ is the initial value, and call integrator to get $x1,y1$, and repeat, $x1,y1$ as initial point, call integrator again, and find root again. Above code's output is not what I expected.

I still don't understand NestList enough, I seem to only know this form, but don’t know how to use it for specific problems.

Update(I still have a bugs with my code, sad, Others gave the right answer, but I still failed)

ClearAll[integrator, myintegrator, stepintegrator];
deltat = 1*^-3;
integrator[x_, y_, {x0_, y0_}] := {x[1], y[1]} /. 
   FindRoot[{x[1] - x[0] == deltat,
      y[1] - y[0] == deltat}, {{x[0], x0}, {y[0], y0}}];
(*integrator[x,y,{0,0}]*)

myintegrator[x_, y_][x0_, 
  y0_] := {Sequence @@ integrator[x, y, {x0, y0}]}
stepintegrator = myintegrator[x, y];
NestList[stepintegrator, {0, 0}, 2]
Improve this question
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  • $\begingroup$ Let's say: f[{x_, y_}] := {x + 1, y + 1}; is a function that takes a list and returns a list. Execute: NestList[f, {x, y}, 4] to see the result. $\endgroup$
    – Syed
    Nov 18, 2021 at 17:39
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    $\begingroup$ read the answer code a bit more closely—you'll notice Michael uses a function as the first argument to nestlist, by expecting myIntegrator[param1, param2,..][{x0, y0}] to return a point in the trajectory. (note that this is of the form f[a][b]—f[a] is a function!) He then takes stepIntegrator = myIntegrator[param1, param2,..], which is, as mentioned, a function. NestList always takes a function as its first argument; see the docs. You should use integrator[x_, y_][{x0_, y0_}] and integrator[x,y] in NestList instead. $\endgroup$
    – thorimur
    Nov 18, 2021 at 17:43
  • $\begingroup$ @thorimur Thank you, it is my first time to know function as ‘function[para,para][x,y]’, you are right, I should read more carefully, it is details can’t be ignored! $\endgroup$
    – Ben
    Nov 18, 2021 at 17:52
  • $\begingroup$ @Syed I have try this code, it doesn’t work when I need update condition, the problem maybe due to ‘f’ should have second parameters like ‘f[para,para][x,y]’ in my example. $\endgroup$
    – Ben
    Nov 18, 2021 at 17:57
  • $\begingroup$ It is a simple example to show how NestList works. NestList can keep applying the function at the last result. $\endgroup$
    – Syed
    Nov 18, 2021 at 18:04

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