Point plot for system of nonlinear equations

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Question:Point plot for system of nonlinear equations

Posted: RezaZanjirani 40 Product: Maple 2021

September 05 2023

Dear Maple experts,

I have a system of several nonlinear equaitons. My code can solve it for a given parameter. But when I want to plot it, it takes too much time with no results. So, I decided to plot it for several given points. I get the answer for the points individually, but I don't know how to apply this to 'plot' command. Would you please help?

$FirmModelPartial1 := proc (alpha, beta, delta) local L1s, qs, ps, prs, hs, `κs`, `λ__1s`, `λ__2s`, `λ__3s`, q, p, pr, h, kappa, `λ__1`, `λ__2`, `λ__3`, FirmpfSiS, RecpfSiS, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, prof1, prof2, L1, L2, E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12; prof1 := (ps-c)*qs+((1/2)*beta^2*`κs`^2/(u*(1-alpha))-(1/2)*(qs+beta*`κs`)^2/u)*(ps-s)+hs*prs*(beta*`κs`-(1/2)*beta^2*`κs`^2/(u*(1-alpha))); L1s := prof1+`λ__1s`*(1-sExp/prs-hs)+`λ__2s`*(qs-`κs`)+`λ__3s`*(qs-alpha*beta*`κs`/(1-alpha)); E1 := qs*(diff(L1s, qs)) = 0; E2 := hs*(diff(L1s, hs)) = 0; E3 := `λ__1s`*(1-sExp/prs-hs) = 0; E4 := `λ__2s`*(qs-`κs`) = 0; E5 := `λ__3s`*(qs-alpha*beta*`κs`/(1-alpha)) = 0; E6 := qs = alpha*u*(v-ps)/(v-s); E7 := prs = ps-delta*v; E8 := `κs` = (beta*prs*(1-hs)+sExp*(1-beta))/(beta^2*(prs*(1-hs)-sExp)/(u*(1-alpha))+2*cr); p, q, pr, h, kappa, `λ__1`, `λ__2`, `λ__3` := (eval([ps, qs, prs, hs, `κs`, `λ__1s`, `λ__2s`, `λ__3s`], solve({0 <= qs-alpha*beta*`κs`/(1-alpha), 0 <= qs-`κs`, 0 <= 1-sExp/prs-hs, 0 <= `λ__1s`, 0 <= `λ__2s`, 0 <= `λ__3s`, diff(L1s, qs) <= 0, diff(L1s, hs) <= 0, c < ps, (1/2)*beta*`κs`/(u*(1-alpha)) < 1, sExp+delta*v < ps, E1, E2, E3, E4, E5, E6, E7, E8}, [ps, qs, prs, hs, `κs`, `λ__1s`, `λ__2s`, `λ__3s`])[1]))[]; xi := kappa/q; FirmpfSiS := max(0, eval(prof1, [ps = p, qs = q, prs = p-delta*v, hs = h, `κs` = kappa])); RecpfSiS := ((1-h)*pr-sExp)*(beta*kappa-(1/2)*beta^2*kappa^2/(u*(1-alpha)))+(sExp-cr)*kappa; UnsoldSiS := (1/2)*(q+beta*kappa)^2/u-(1/2)*beta^2*kappa^2/(u*(1-alpha)); EnvironSiS := q+UnsoldSiS; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, h, UnsoldSiS, h, xi end proc$