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Welcome all, I have a comment to explain how my system solver. My response was to add

Method -> {"FixedStep", 
    Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4}}, 
  StartingStepSize -> 0.125, MaxStep->Infinity]`

in NDSolve.

In the paper, the method is indicated as a fourth-order Runge–Kutta was used by choosing a unit of time in the form of 30 days in addition to 0.125 integration steps per 3 hours But the Reviewer ignores my response. Actually, it is better to solve my system by the fixed-step method. Hence, what is the problem in my response? and how to reply to the reviewer as well to get my paper accepted. Is there any simple specific fixed step of Runge-Kutta?

sy11 = {N1'[t] == 
        r N1[t] (1 - β1 N1[t]) - η N1[t] I1[t] - β2 N1[
           t] T[t], 
       T'[t] == α1 T[t] (1 - α2 T[t]) + α3 N1[t] T[
           t] - α4 T[t] I1[t], 
       I1'[t] == σ - δ I1[t] + (ρ N1[t] I1[t])/(
         m1 + N1[t]) - μ1 N1[t] I1[t] - μ2 T[t] I1[
           t] + (ρ2 T[t] I1[t])/(m2 + T[t])};
    co11 = {N1[0] == 1, T[0] == 1, I1[0] == 1.22};
    residuals1 = sy22 /. Equal -> Subtract;
    sol22 = NDSolve[{sy11, co11}, {N1, T, I1}, {t, 0, 30}, 
        Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4}, 
      StartingStepSize -> 0.125]
flinty
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sana alharbi
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  • Is there any simple specific fixed step of Runge-Kutta? I don't know a lot about it, but maybe StepSizeRatioBounds->{1,1} would keep the step fixed? There are a lot of missing details in your code, such as the definitions of all the constants and sy22. Without these nobody can run it to check if what you're doing is sensible. – flinty Jul 19 '20 at 20:30
  • you can remove residuals1 = sy22 /. Equal -> Subtract . and the constants are arbitrary. The code is run well. My question is how can answer the following question: please, explain the choice of ODE solver for your task. Was it fixed or variable stepsize? How you took into account the effects caused by the choice of numerical integration method?. all reviewers are asking me the same question. @flinty – sana alharbi Jul 19 '20 at 20:49
  • So why did you choose ExplicitRungeKutta, rather than another method? By default "ExplicitRungeKutta" seems to have a variable step size - that's all I can say. – flinty Jul 19 '20 at 20:53
  • Actually, I don't known that before. I did a test to add Method -> {"FixedStep", Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4}}, StartingStepSize -> 0.125 in NDSolve and have tha same result and the code worked as well as same as ImplicitRungeKutta.@flinty – sana alharbi Jul 19 '20 at 21:09
  • Why do you ask essentially the same question once again? – xzczd Jul 20 '20 at 05:33
  • The reviewer Reject my response and asked me to explain how the system s solver by Mathematica? he ignored the stepsize and the method an Infinity of MaxSteps @xzczd – sana alharbi Jul 20 '20 at 08:29
  • If the reviewer cares about such stuff, he'll reject of course, because Method -> {"ExplicitRungeKutta", "DifferenceOrder" -> 4} still leads to a blackbox. You should follow my advice here to choose classical RK4. – xzczd Jul 20 '20 at 08:36

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