# Solve the following partial differential equation?

Posted 5 months ago
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 Consider the following code: In[1]:= Subscript[a, 11] = 1.0 Out[1]= 1. In[2]:= Subscript[a, 12] = 0.0015 Out[2]= 0.0015 In[3]:= Subscript[a, 13] = 0.0055 Out[3]= 0.0055 In[4]:= Subscript[a, 21] = 0.5 Out[4]= 0.5 In[5]:= Subscript[a, 22] = 0.00025 Out[5]= 0.00025 In[6]:= Subscript[a, 23] = 0.0055 Out[6]= 0.0055 In[7]:= Subscript[d, 1] = 0.23 Out[7]= 0.23 In[8]:= Subscript[d, 2] = 0.45 Out[8]= 0.45 In[9]:= j = NDSolveValue[{D[u[x, \[Psi]], \[Psi], \[Psi]] == 0, u[x, -1] == u[x, 1] == u[-1, \[Psi]] == u[1, \[Psi]] == 0}, u, {x, -1, 1}, {\[Psi], -1, 1}] Out[9]= InterpolatingFunction[{{-1., 1.}, {-1., 1.}}, <>] In[10]:= k = NDSolveValue[{D[u[y, \[Psi]], \[Psi], \[Psi]] == 0, u[y, -1] == u[y, 1] == u[-1, \[Psi]] == u[1, \[Psi]] == 0}, u, {y, -1, 1}, {\[Psi], -1, 1}] Out[10]= InterpolatingFunction[{{-1., 1.}, {-1., 1.}}, <>] In[12]:= Equationp = NDSolve[{x'[t] == Subscript[a, 11] x[t] - Subscript[a, 12] x[t]^2 - Subscript[a, 13] x[t] y[t] + Subscript[d, 1] j[t], y'[t] == -Subscript[a, 21] y[t] - Subscript[a, 22] y[t]^2 + Subscript[a, 23] x[t] y[t] + Subscript[d, 2] k[t], x[0] == 10, y[0] == 5, \[Psi][0] == 5, D[u[x, \[Psi]], \[Psi]] == 10, D[u[y, \[Psi]], \[Psi]] == 5}, {x, y, \[Psi]}, {\[Psi], 0, 2 \[Pi]}, {t, 0, 25}] During evaluation of In[12]:= NDSolve::dsfun: [Psi] cannot be used as a function. Attachments:
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Posted 5 months ago
 Is Psi an independent variable or an unknown function? What are j[t] and u[x,Psi]?