fsolve in iteration - MaplePrimes

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Question:fsolve in iteration

Posted: shimaa sadk 45 Product: Maple

July 13 2018

here my loop; after 8 iteration maple couldnt solve the equations and give me this error .
Is there any method to garentee that fsolve could work intire the 1000 iteration

Download exp_new_for_alpha_more_than_22.mw

with(LinearAlgebra):

f[1] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(n, 1/R), sum(x[i], i = 1 .. n)), VectorCalculus:-`-`(sum(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`+`(2, a[i]), x[i]), exp(VectorCalculus:-`*`(R, x[i]))), 1/VectorCalculus:-`+`(VectorCalculus:-`+`(exp(VectorCalculus:-`*`(R, x[i])), -1), Q)), i = 1 .. n))):

f[2] := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(m, 1/S), sum(y[j], j = 1 .. m)), VectorCalculus:-`-`(sum(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`+`(2, b[j]), y[j]), exp(VectorCalculus:-`*`(y[j], S))), 1/VectorCalculus:-`+`(VectorCalculus:-`+`(exp(VectorCalculus:-`*`(y[j], S)), -1), Q)), j = 1 .. m))):

a := [seq(0, i = 1 .. 21), 2, 2, 1, seq(0, i = 1 .. 21)]:

$for so from 0 to K do W := GenerateUniform(n, 0, 1); for iii to n do vv[iii] := W[iii]^(1/(iii+sum(a[jjj], jjj = n-iii+1 .. n))) end do; for sss to n do uu[sss] := 1-product(vv[n-jjj+1], jjj = 1 .. sss); x[sss] := fsolve(1-3/(exp(.3*t)-(1-3)) = uu[sss], t = 0 .. infinity) end do; U := GenerateUniform(m, 0, 1); for ii to m do v[ii] := U[ii]^(1/(ii+sum(b[jj], jj = m-ii+1 .. m))) end do; for ss to m do u[ss] := 1-product(v[m-jj+1], jj = 1 .. ss); y[ss] := fsolve(1-3/(exp(.1*t)-(1-3)) = u[ss], t = 0 .. infinity) end do; c := describe[quartile[1]]([seq(x[i], i = 1 .. n)]); cc := describe[quartile[3]]([seq(x[i], i = 1 .. n)]); L := describe[quartile[1]]([seq(y[i], i = 1 .. m)]); LL := describe[quartile[3]]([seq(y[i], i = 1 .. m)]); R[1] := fsolve(9*exp(R*c)-exp(R*cc) = 8, R = 0 .. infinity); S[1] := fsolve(9*exp(S*L)-exp(S*LL) = 8, S = 0 .. infinity); Q[1] := 3*(exp(R[1]*c)-1+(exp(S[1]*L)-1))*(1/2); for h to 40 while `and`(`and`(`and`(`and`(`and`(abs(E1[h]) > 0.5e-3, abs(E2[h]) > 0.5e-3), abs(E3[h]) > 0.5e-3), Q[h] > 2), S[h] > 0), R[h] > 0) do Q[h+1] := fsolve(eval(f[3], {R = R[h], S = S[h]}) = 0, Q = 2 .. infinity); R[h+1] := fsolve(eval(f[1], Q = Q[h+1]) = 0, R = 0 .. infinity); S[h+1] := fsolve(eval(f[2], Q = Q[h+1]) = 0, S = 0 .. infinity); KK := Matrix([[R[h]], [S[h]], [Q[h]]]); E1[h+1] := abs(R[h+1]-R[h]); E2[h+1] := abs(S[h+1]-S[h]); E3[h+1] := abs(Q[h+1]-Q[h]) end do; A[so] := Determinant(KK[1]); B[so] := Determinant(KK[2]); C[so] := Determinant(KK[3]); P[so] := simplify(int(A[so]*C[so]^2*exp(A[so]*x)/((exp(A[so]*x)-1+C[so])^2*(exp(B[so]*x)-1+C[so])), x = 0 .. infinity, numeric)) end do$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$W := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

$U := Vector(4, {(1) = ` 1 .. 45 `*Array, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*C_order})$

Error, (in fsolve) Q is in the equation, and is not solved for

a := [seq(A[i], i = 1 .. 1000)]:

for i to 1000 do aa_[i] := `if`(0 < P[i] and P[i] < 1, a[i], 0); bb_[i] := `if`(0 < P[i] and P[i] < 1, b[i], 0); cc_[i] := `if`(0 < P[i] and P[i] < 1, c[i], 0); gg_[i] := `if`(0 < P[i] and P[i] < 1, p[i], 0) end do:

Tau := [seq(aa_[i], i = 1 .. 1000)]:

rr := [seq(`if`(Tau[i] = 0, NULL, i), i = 1 .. 1000)]:

r := Tau[rr]:

(1)

lambda[1] := Mean([seq(r[i], i = 1 .. nops(r))]); lambda[2] := Mean([seq(s[i], i = 1 .. nops(s))]); alpha := Mean([seq(q[i], i = 1 .. nops(q))]); Pro := Mean([seq(w[i], i = 1 .. nops(w))]); Bi_ := .647737-Pro; ME_ := Bi_^2