I have developed a code for solving differential equations and I have been trying to solve it using the ModelingToolkit package and the MethodOfLines:
begin @parameters t, r, x
`@variables T(…)
Dr=Differential(r)
Drr=Differential(r)^2
Dx=Differential(x)
Dxx=Differential(x)^2
Dt=Differential(t)
Dtt=Differential(t)^2
#Discretization parameters
nr1 = 30
r1= range(0.0, 0.0015, length=(nr1))
dr=((0.0015)-0)/(nr1-1)
x1= range(0.0, 0.130, length=(nr1))
dx= ((0.130)-0)/(nr1-1)
#equation
eq=[Dt(T(t,r,x)) ~ -VDx(T(t,r,x)) - (1/r)Dr(αrDr(T(t,r,x))) - ρCpDxx(T(t,r,x)) + Qv]
#BC
bcs=[Dr(T(t,0.0,x))~0,
Dr(T(t,0.0015,x))~0,
Dx(T(t,r,0.0))~0,
-kDx(T(t,r,0.130))~ 0,
#-Q - αA*((T(t,r,0.130))-Ts) + ϵσ((T(t,0.0015,x))^4-(Ts)^4)),
Dt(T(0.0,r,x))~T1]
#space and time domain
domains=[t ∈ Interval(0.0, 6373.0),
r ∈ Interval(0.0, 0.0015),
x ∈ Interval(0.0, 0.130)]
@named pdesys = PDESystem(eq, bcs, domains, [t,r,x], [T(t,r,x)])
end`
However, I am getting this error:
“ArgumentError: SymbolicUtils.BasicSymbolic{Real}[(T(t))[2, 2], (T(t))[3, 2], (T(t))[4, 2], (T(t))[5, 2], (T(t))[6, 2], (T(t))[7, 2], (T(t))[8, 2], (T(t))[9, 2], (T(t))[10, 2], (T(t))[11, 2], (T(t))[12, 2], (T(t))[13, 2], (T(t))[14, 2], (T(t))[15, 2], (T(t))[16, 2], (T(t))[17, 2], (T(t))[18, 2], (T(t))[19, 2], (T(t))[20, 2], (T(t))[21, 2], (T(t))[22, 2], (T(t))[23, 2], (T(t))[24, 2], (T(t))[25, 2], (T(t))[26, 2], (T(t))[27, 2], (T(t))[28, 2], (T(t))[29, 2], (T(t))[2, 3], (T(t))[3, 3], (T(t))[4, 3], (T(t))[5, 3], (T(t))[6, 3], (T(t))[7, 3], (T(t))[8, 3], (T(t))[9, 3], (T(t))[10, 3], (T(t))[11, 3], (T(t))[12, 3], (T(t))[13, 3], (T(t))[14, 3], (T(t))[15, 3], (T(t))[16, 3], (T(t))[17, 3], (T(t))[18, 3], (T(t))[19, 3], (T(t))[20, 3], (T(t))[21, 3], (T(t))[22, 3], (T(t))[23, 3], (T(t))[24, 3], (T(t))[25, 3], (T(t))[26, 3], (T(t))[27, 3], (T(t))[28, 3], (T(t))[29, 3], (T(t))[2, 4], (T(t))[3, 4], (T(t))[4, 4], (T(t))[5, 4], (T(t))[6, 4], (T(t))[7, 4], (T(t))[8, 4], (T(t))[9, 4], (T(t))[10, 4], (T(t))[11, 4], (T(t))[12, 4], (T(t))[13, 4], (T(t))[14, 4], (T(t))[15, 4], (T(t))[16, 4], (T(t))[17, 4], (T(t))[18, 4], (T(t))[19, 4], (T(t))[20, 4], (T(t))[21, 4], (T(t))[22, 4], (T(t))[23, 4], (T(t))[24, 4], (T(t))[25, 4], (T(t))[26, 4], (T(t))[27, 4], (T(t))[28, 4], (T(t))[29, 4], (T(t))[2, 5], (T(t))[3, 5], (T(t))[4, 5], (T(t))[5, 5], (T(t))[6, 5], (T(t))[7, 5], (T(t))[8, 5], (T(t))[9, 5], (T(t))[10, 5], (T(t))[11, 5], (T(t))[12, 5], (T(t))[13, 5], (T(t))[14, 5], (T(t))[15, 5], (T(t))[16, 5], (T(t))[17, 5], (T(t))[18, 5], (T(t))[19, 5], (T(t))[20, 5], (T(t))[21, 5], (T(t))[22, 5], (T(t))[23, 5], (T(t))[24, 5], (T(t))[25, 5], (T(t))[26, 5], (T(t))[27, 5], (T(t))[28, 5], (T(t))[29, 5], (T(t))[2, 6], (T(t))[3, 6], (T(t))[4, 6], (T(t))[5, 6], (T(t))[6, 6], (T(t))[7, 6], (T(t))[8, 6], (T(t))[9, 6], (T(t))[10, 6], (T(t))[11, 6], (T(t))[12, 6], (T(t))[13, 6], (T(t))[14, 6], (T(t))[15, 6], (T(t))[16, 6], (T(t))[17, 6], (T(t))[18, 6], (T(t))[19, 6], (T(t))[20, 6], (T(t))[21, 6], (T(t))[22, 6], (T(t))[23, 6], (T(t))[24, 6], (T(t))[25, 6], (T(t))[26, 6], (T(t))[27, 6], (T(t))[28, 6], (T(t))[29, 6], (T(t))[2, 7], (T(t))[3, 7], (T(t))[4, 7], (T(t))[5, 7], (T(t))[6, 7], (T(t))[7, 7], (T(t))[8, 7], (T(t))[9, 7], (T(t))[10, 7], (T(t))[11, 7], (T(t))[12, 7], (T(t))[13, 7], (T(t))[14, 7], (T(t))[15, 7], (T(t))[16, 7], (T(t))[17, 7], (T(t))[18, 7], (T(t))[19, 7], (T(t))[20, 7], (T(t))[21, 7], (T(t))[22, 7], (T(t))[23, 7], (T(t))[24, 7], (T(t))[25, 7], (T(t))[26, 7], (T(t))[27, 7], (T(t))[28, 7], (T(t))[29, 7], (T(t))[2, 8], (T(t))[3, 8], (T(t))[4, 8], (T(t))[5, 8], (T(t))[6, 8], (T(t))[7, 8], (T(t))[8, 8], (T(t))[9, 8], (T(t))[10, 8], (T(t))[11, 8], (T(t))[12, 8], (T(t))[13, 8], (T(t))[14, 8], (T(t))[15, 8], (T(t))[16, 8], (T(t))[17, 8], (T(t))[18, 8], (T(t))[19, 8], (T(t))[20, 8], (T(t))[21, 8], (T(t))[22, 8], (T(t))[23, 8], (T(t))[24, 8], (T(t))[25, 8], (T(t))[26, 8], (T(t))[27, 8], (T(t))[28, 8], (T(t))[29, 8], (T(t))[2, 9], (T(t))[3, 9], (T(t))[4, 9], (T(t))[5, 9], (T(t))[6, 9], (T(t))[7, 9], (T(t))[8, 9], (T(t))[9, 9], (T(t))[10, 9], (T(t))[11, 9], (T(t))[12, 9], (T(t))[13, 9], (T(t))[14, 9], (T(t))[15, 9], (T(t))[16, 9], (T(t))[17, 9], (T(t))[18, 9], (T(t))[19, 9], (T(t))[20, 9], (T(t))[21, 9], (T(t))[22, 9], (T(t))[23, 9], (T(t))[24, 9], (T(t))[25, 9], (T(t))[26, 9], (T(t))[27, 9], (T(t))[28, 9], (T(t))[29, 9], (T(t))[2, 10], (T(t))[3, 10], (T(t))[4, 10], (T(t))[5, 10], (T(t))[6, 10], (T(t))[7, 10], (T(t))[8, 10], (T(t))[9, 10], (T(t))[10, 10], (T(t))[11, 10], (T(t))[12, 10], (T(t))[13, 10], (T(t))[14, 10], (T(t))[15, 10], (T(t))[16, 10], (T(t))[17, 10], (T(t))[18, 10], (T(t))[19, 10], (T(t))[20, 10], (T(t))[21, 10], (T(t))[22, 10], (T(t))[23, 10], (T(t))[24, 10], (T(t))[25, 10], (T(t))[26, 10], (T(t))[27, 10], (T(t))[28, 10], (T(t))[29, 10], (T(t))[2, 11], (T(t))[3, 11], (T(t))[4, 11], (T(t))[5, 11], (T(t))[6, 11], (T(t))[7, 11], (T(t))[8, 11], (T(t))[9, 11], (T(t))[10, 11], (T(t))[11, 11], (T(t))[12, 11], (T(t))[13, 11], (T(t))[14, 11], (T(t))[15, 11], (T(t))[16, 11], (T(t))[17, 11], (T(t))[18, 11], (T(t))[19, 11], (T(t))[20, 11], (T(t))[21, 11], (T(t))[22, 11], (T(t))[23, 11], (T(t))[24, 11], (T(t))[25, 11], (T(t))[26, 11], (T(t))[27, 11], (T(t))[28, 11], (T(t))[29, 11], (T(t))[2, 12], (T(t))[3, 12], (T(t))[4, 12], (T(t))[5, 12], (T(t))[6, 12], (T(t))[7, 12], (T(t))[8, 12], (T(t))[9, 12], (T(t))[10, 12], (T(t))[11, 12], (T(t))[12, 12], (T(t))[13, 12], (T(t))[14, 12], (T(t))[15, 12], (T(t))[16, 12], (T(t))[17, 12], (T(t))[18, 12], (T(t))[19, 12], (T(t))[20, 12], (T(t))[21, 12], (T(t))[22, 12], (T(t))[23, 12], (T(t))[24, 12], (T(t))[25, 12], (T(t))[26, 12], (T(t))[27, 12], (T(t))[28, 12], (T(t))[29, 12], (T(t))[2, 13], (T(t))[3, 13], (T(t))[4, 13], (T(t))[5, 13], (T(t))[6, 13], (T(t))[7, 13], (T(t))[8, 13], (T(t))[9, 13], (T(t))[10, 13], (T(t))[11, 13], (T(t))[12, 13], (T(t))[13, 13], (T(t))[14, 13], (T(t))[15, 13], (T(t))[16, 13], (T(t))[17, 13], (T(t))[18, 13], (T(t))[19, 13], (T(t))[20, 13], (T(t))[21, 13], (T(t))[22, 13], (T(t))[23, 13], (T(t))[24, 13], (T(t))[25, 13], (T(t))[26, 13], (T(t))[27, 13], (T(t))[28, 13], (T(t))[29, 13], (T(t))[2, 14], (T(t))[3, 14], (T(t))[4, 14], (T(t))[5, 14], (T(t))[6, 14], (T(t))[7, 14], (T(t))[8, 14], (T(t))[9, 14], (T(t))[10, 14], (T(t))[11, 14], (T(t))[12, 14], (T(t))[13, 14], (T(t))[14, 14], (T(t))[15, 14], (T(t))[16, 14], (T(t))[17, 14], (T(t))[18, 14], (T(t))[19, 14], (T(t))[20, 14], (T(t))[21, 14], (T(t))[22, 14], (T(t))[23, 14], (T(t))[24, 14], (T(t))[25, 14], (T(t))[26, 14], (T(t))[27, 14], (T(t))[28, 14], (T(t))[29, 14], (T(t))[2, 15], (T(t))[3, 15], (T(t))[4, 15], (T(t))[5, 15], (T(t))[6, 15], (T(t))[7, 15], (T(t))[8, 15], (T(t))[9, 15], (T(t))[10, 15], (T(t))[11, 15], (T(t))[12, 15], (T(t))[13, 15], (T(t))[14, 15], (T(t))[15, 15], (T(t))[16, 15], (T(t))[17, 15], (T(t))[18, 15], (T(t))[19, 15], (T(t))[20, 15], (T(t))[21, 15], (T(t))[22, 15], (T(t))[23, 15], (T(t))[24, 15], (T(t))[25, 15], (T(t))[26, 15], (T(t))[27, 15], (T(t))[28, 15], (T(t))[29, 15], (T(t))[2, 16], (T(t))[3, 16], (T(t))[4, 16], (T(t))[5, 16], (T(t))[6, 16], (T(t))[7, 16], (T(t))[8, 16], (T(t))[9, 16], (T(t))[10, 16], (T(t))[11, 16], (T(t))[12, 16], (T(t))[13, 16], (T(t))[14, 16], (T(t))[15, 16], (T(t))[16, 16], (T(t))[17, 16], (T(t))[18, 16], (T(t))[19, 16], (T(t))[20, 16], (T(t))[21, 16], (T(t))[22, 16], (T(t))[23, 16], (T(t))[24, 16], (T(t))[25, 16], (T(t))[26, 16], (T(t))[27, 16], (T(t))[28, 16], (T(t))[29, 16], (T(t))[2, 17], (T(t))[3, 17], (T(t))[4, 17], (T(t))[5, 17], (T(t))[6, 17], (T(t))[7, 17], (T(t))[8, 17], (T(t))[9, 17], (T(t))[10, 17], (T(t))[11, 17], (T(t))[12, 17], (T(t))[13, 17], (T(t))[14, 17], (T(t))[15, 17], (T(t))[16, 17], (T(t))[17, 17], (T(t))[18, 17], (T(t))[19, 17], (T(t))[20, 17], (T(t))[21, 17], (T(t))[22, 17], (T(t))[23, 17], (T(t))[24, 17], (T(t))[25, 17], (T(t))[26, 17], (T(t))[27, 17], (T(t))[28, 17], (T(t))[29, 17], (T(t))[2, 18], (T(t))[3, 18], (T(t))[4, 18], (T(t))[5, 18], (T(t))[6, 18], (T(t))[7, 18], (T(t))[8, 18], (T(t))[9, 18], (T(t))[10, 18], (T(t))[11, 18], (T(t))[12, 18], (T(t))[13, 18], (T(t))[14, 18], (T(t))[15, 18], (T(t))[16, 18], (T(t))[17, 18], (T(t))[18, 18], (T(t))[19, 18], (T(t))[20, 18], (T(t))[21, 18], (T(t))[22, 18], (T(t))[23, 18], (T(t))[24, 18], (T(t))[25, 18], (T(t))[26, 18], (T(t))[27, 18], (T(t))[28, 18], (T(t))[29, 18], (T(t))[2, 19], (T(t))[3, 19], (T(t))[4, 19], (T(t))[5, 19], (T(t))[6, 19], (T(t))[7, 19], (T(t))[8, 19], (T(t))[9, 19], (T(t))[10, 19], (T(t))[11, 19], (T(t))[12, 19], (T(t))[13, 19], (T(t))[14, 19], (T(t))[15, 19], (T(t))[16, 19], (T(t))[17, 19], (T(t))[18, 19], (T(t))[19, 19], (T(t))[20, 19], (T(t))[21, 19], (T(t))[22, 19], (T(t))[23, 19], (T(t))[24, 19], (T(t))[25, 19], (T(t))[26, 19], (T(t))[27, 19], (T(t))[28, 19], (T(t))[29, 19], (T(t))[2, 20], (T(t))[3, 20], (T(t))[4, 20], (T(t))[5, 20], (T(t))[6, 20], (T(t))[7, 20], (T(t))[8, 20], (T(t))[9, 20], (T(t))[10, 20], (T(t))[11, 20], (T(t))[12, 20], (T(t))[13, 20], (T(t))[14, 20], (T(t))[15, 20], (T(t))[16, 20], (T(t))[17, 20], (T(t))[18, 20], (T(t))[19, 20], (T(t))[20, 20], (T(t))[21, 20], (T(t))[22, 20], (T(t))[23, 20], (T(t))[24, 20], (T(t))[25, 20], (T(t))[26, 20], (T(t))[27, 20], (T(t))[28, 20], (T(t))[29, 20], (T(t))[2, 21], (T(t))[3, 21], (T(t))[4, 21], (T(t))[5, 21], (T(t))[6, 21], (T(t))[7, 21], (T(t))[8, 21], (T(t))[9, 21], (T(t))[10, 21], (T(t))[11, 21], (T(t))[12, 21], (T(t))[13, 21], (T(t))[14, 21], (T(t))[15, 21], (T(t))[16, 21], (T(t))[17, 21], (T(t))[18, 21], (T(t))[19, 21], (T(t))[20, 21], (T(t))[21, 21], (T(t))[22, 21], (T(t))[23, 21], (T(t))[24, 21], (T(t))[25, 21], (T(t))[26, 21], (T(t))[27, 21], (T(t))[28, 21], (T(t))[29, 21], (T(t))[2, 22], (T(t))[3, 22], (T(t))[4, 22], (T(t))[5, 22], (T(t))[6, 22], (T(t))[7, 22], (T(t))[8, 22], (T(t))[9, 22], (T(t))[10, 22], (T(t))[11, 22], (T(t))[12, 22], (T(t))[13, 22], (T(t))[14, 22], (T(t))[15, 22], (T(t))[16, 22], (T(t))[17, 22], (T(t))[18, 22], (T(t))[19, 22], (T(t))[20, 22], (T(t))[21, 22], (T(t))[22, 22], (T(t))[23, 22], (T(t))[24, 22], (T(t))[25, 22], (T(t))[26, 22], (T(t))[27, 22], (T(t))[28, 22], (T(t))[29, 22], (T(t))[2, 23], (T(t))[3, 23], (T(t))[4, 23], (T(t))[5, 23], (T(t))[6, 23], (T(t))[7, 23], (T(t))[8, 23], (T(t))[9, 23], (T(t))[10, 23], (T(t))[11, 23], (T(t))[12, 23], (T(t))[13, 23], (T(t))[14, 23], (T(t))[15, 23], (T(t))[16, 23], (T(t))[17, 23], (T(t))[18, 23], (T(t))[19, 23], (T(t))[20, 23], (T(t))[21, 23], (T(t))[22, 23], (T(t))[23, 23], (T(t))[24, 23], (T(t))[25, 23], (T(t))[26, 23], (T(t))[27, 23], (T(t))[28, 23], (T(t))[29, 23], (T(t))[2, 24], (T(t))[3, 24], (T(t))[4, 24], (T(t))[5, 24], (T(t))[6, 24], (T(t))[7, 24], (T(t))[8, 24], (T(t))[9, 24], (T(t))[10, 24], (T(t))[11, 24], (T(t))[12, 24], (T(t))[13, 24], (T(t))[14, 24], (T(t))[15, 24], (T(t))[16, 24], (T(t))[17, 24], (T(t))[18, 24], (T(t))[19, 24], (T(t))[20, 24], (T(t))[21, 24], (T(t))[22, 24], (T(t))[23, 24], (T(t))[24, 24], (T(t))[25, 24], (T(t))[26, 24], (T(t))[27, 24], (T(t))[28, 24], (T(t))[29, 24], (T(t))[2, 25], (T(t))[3, 25], (T(t))[4, 25], (T(t))[5, 25], (T(t))[6, 25], (T(t))[7, 25], (T(t))[8, 25], (T(t))[9, 25], (T(t))[10, 25], (T(t))[11, 25], (T(t))[12, 25], (T(t))[13, 25], (T(t))[14, 25], (T(t))[15, 25], (T(t))[16, 25], (T(t))[17, 25], (T(t))[18, 25], (T(t))[19, 25], (T(t))[20, 25], (T(t))[21, 25], (T(t))[22, 25], (T(t))[23, 25], (T(t))[24, 25], (T(t))[25, 25], (T(t))[26, 25], (T(t))[27, 25], (T(t))[28, 25], (T(t))[29, 25], (T(t))[2, 26], (T(t))[3, 26], (T(t))[4, 26], (T(t))[5, 26], (T(t))[6, 26], (T(t))[7, 26], (T(t))[8, 26], (T(t))[9, 26], (T(t))[10, 26], (T(t))[11, 26], (T(t))[12, 26], (T(t))[13, 26], (T(t))[14, 26], (T(t))[15, 26], (T(t))[16, 26], (T(t))[17, 26], (T(t))[18, 26], (T(t))[19, 26], (T(t))[20, 26], (T(t))[21, 26], (T(t))[22, 26], (T(t))[23, 26], (T(t))[24, 26], (T(t))[25, 26], (T(t))[26, 26], (T(t))[27, 26], (T(t))[28, 26], (T(t))[29, 26], (T(t))[2, 27], (T(t))[3, 27], (T(t))[4, 27], (T(t))[5, 27], (T(t))[6, 27], (T(t))[7, 27], (T(t))[8, 27], (T(t))[9, 27], (T(t))[10, 27], (T(t))[11, 27], (T(t))[12, 27], (T(t))[13, 27], (T(t))[14, 27], (T(t))[15, 27], (T(t))[16, 27], (T(t))[17, 27], (T(t))[18, 27], (T(t))[19, 27], (T(t))[20, 27], (T(t))[21, 27], (T(t))[22, 27], (T(t))[23, 27], (T(t))[24, 27], (T(t))[25, 27], (T(t))[26, 27], (T(t))[27, 27], (T(t))[28, 27], (T(t))[29, 27], (T(t))[2, 28], (T(t))[3, 28], (T(t))[4, 28], (T(t))[5, 28], (T(t))[6, 28], (T(t))[7, 28], (T(t))[8, 28], (T(t))[9, 28], (T(t))[10, 28], (T(t))[11, 28], (T(t))[12, 28], (T(t))[13, 28], (T(t))[14, 28], (T(t))[15, 28], (T(t))[16, 28], (T(t))[17, 28], (T(t))[18, 28], (T(t))[19, 28], (T(t))[20, 28], (T(t))[21, 28], (T(t))[22, 28], (T(t))[23, 28], (T(t))[24, 28], (T(t))[25, 28], (T(t))[26, 28], (T(t))[27, 28], (T(t))[28, 28], (T(t))[29, 28], (T(t))[2, 29], (T(t))[3, 29], (T(t))[4, 29], (T(t))[5, 29], (T(t))[6, 29], (T(t))[7, 29], (T(t))[8, 29], (T(t))[9, 29], (T(t))[10, 29], (T(t))[11, 29], (T(t))[12, 29], (T(t))[13, 29], (T(t))[14, 29], (T(t))[15, 29], (T(t))[16, 29], (T(t))[17, 29], (T(t))[18, 29], (T(t))[19, 29], (T(t))[20, 29], (T(t))[21, 29], (T(t))[22, 29], (T(t))[23, 29], (T(t))[24, 29], (T(t))[25, 29], (T(t))[26, 29], (T(t))[27, 29], (T(t))[28, 29], (T(t))[29, 29]] are missing from the variable map.”