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Mathematics Calculus Wolfram Language Numerical Computation

Compute values of the following dependent functions?

Fabi An

Posted 4 years ago

Hello, I want to compute values of the functions v and R. To compute v, I need R and to compute R, I need v. v[t_?NumberQ] := v[t] = Exp[NIntegrate[-f[v[s]^2, R[s]], {s, 0, t}]] R[t_?NumberQ] := R[t] = NIntegrate[h[v[s], R[s]]* w[s], {s, 0, t}] + v[t] * w[t] - NIntegrate[(h[v[t], R[t]] )^2, {s, 0, t}]. Can anybody help me? Thanks..

POSTED BY: Fabi An

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Fabi An

Posted 4 years ago

You integrate from 0 to t. The expression is correct. The function R is defined in the last line.

POSTED BY: Fabi An

Anonymous User

Posted 4 years ago

NIntegrate[-f[v[s]^2, R[s]], {s, 0, t}] NIntegrate[ expr, range(s) ] R[s] does not have the form {s, min, max}. Please check the syntax. As things are you have not posted your equations yet because in that form we cannot say what you intended.

POSTED BY: Anonymous User

Anonymous User

Posted 4 years ago

NIntegrate[-f[v[s]^2, R[s]], {s, 0, t}] NIntegrate[ expr, range(s) ] Are you implying that R[s] as defined above is in the form {s, min, max}. If not, please check the syntax. As things are you have not posted your equations yet.

POSTED BY: Anonymous User

Fabi An

Posted 4 years ago

Enter code here pde = (-3/2) * 1* y[x, t] * D[y[x, t], t] + 1/(4y[x, t]) D[D[y[x, t], t], t] - D[y[x, t], x] == 0 sol2 = NDSolve[{pde, y[0, t] == Sqrt[(1.5 + Tanh[t - 100])^2]}, y[x, t], {x, 0, 1}, {t, 0, 100}] data = RandomFunction[WienerProcess[], {0, 10, 0.1}] w[t_] := process["PathFunction"] [t] f[x_, t_] = y[x, t] /. sol2[[1]] h[x_, t_] := f[x^2, t] * x v[t_?NumberQ] := v[t] = Exp[NIntegrate[-f[v[s]^2, R[s]], {s, 0, t}]] R[t_?NumberQ] := R[t] = NIntegrate[h[v[s], R[s]]* w[s], {s, 0, t}] + v[t] * w[t] - NIntegrate[(h[v[t], R[t]] )^2, {s, 0, t}]

Enter code here

pde = (-3/2) * 1* y[x, t] * D[y[x, t], t] + 
   1/(4*y[x, t]) * D[D[y[x, t], t], t] - D[y[x, t], x] == 0

sol2 = NDSolve[{pde, y[0, t] == Sqrt[(1.5 + Tanh[t - 100])^2]}, 
  y[x, t], {x, 0, 1}, {t, 0, 100}]

data = RandomFunction[WienerProcess[], {0, 10, 0.1}]

w[t_] := process["PathFunction"] [t]

f[x_, t_] = y[x, t] /. sol2[[1]]

h[x_, t_] := f[x^2, t] * x

v[t_?NumberQ] := v[t] = Exp[NIntegrate[-f[v[s]^2, R[s]], {s, 0, t}]]

R[t_?NumberQ] := R[t] = NIntegrate[h[v[s], R[s]]* w[s], {s, 0, t}] + v[t] * w[t] - NIntegrate[(h[v[t], R[t]] )^2, {s, 0, t}]

POSTED BY: Fabi An