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Question: error message'' which is not valid for its 1st argument, expr''''

Question:error message'' which is not valid for its 1st argument, expr''''

torabi 80 Maple 2016
syntax
December 03 2016
0

hi

how i can remove this error?

1) ''Error, invalid input: lhs received diff(diff(diff(diff(w(x, y, t), x), x), x), x)+.12*(diff(diff(diff(diff(w(x, y, t), x), x), y), y))+0.11e-2*(diff(diff(diff(diff(w(x, y, t), y), y), y), y))+10-.4*(diff(diff(w(x, y, t), x), x))-0.4e-2*(diff(diff(w(x, y, t), y), y))+diff(diff(w(x, y, t), t), t)-w(x, y, t)-tau, which is not valid for its 1st argument, expr'''''

2)'' Error, incorrect number of extra arguments in select''

thanks

scale.mw
 

 

NULL

> 

restart:Digits := 15: beta := 1: alpha := 0.1: Upsilon := .1: xi := 10: eta := .1: N_X := .4: N_Y := .4: psi:NULL=4.73:tau = 10

tau = 10

 (1)
> 

A5 := 1; A6 := 2*alpha^2; A7 := alpha^4; A8 := xi; A9 := xi*alpha^2; A10 := xi*alpha^4; A11 := -N_X; A12 := -N_Y*alpha^2; A13 := 1; A14 := -beta; A15 := -tau

-tau

 (2)
> 

EOM := A5*(diff(w(x, y, t), x, x, x, x))+A6*(diff(w(x, y, t), x, x, y, y))+A7*(diff(w(x, y, t), y, y, y, y))+A8(diff(w(x, y, t), x, x, x, x))+A9*(diff(w(x, y, t), x, x, y, y))+A10*(diff(w(x, y, t), y, y, y, y))+A11*(diff(w(x, y, t), x, x))+A12*(diff(w(x, y, t), y, y))+A13*(diff(w(x, y, t), t, t))+A14*w(x, y, t)+A15

diff(diff(diff(diff(w(x, y, t), x), x), x), x)+.12*(diff(diff(diff(diff(w(x, y, t), x), x), y), y))+0.11e-2*(diff(diff(diff(diff(w(x, y, t), y), y), y), y))+10-.4*(diff(diff(w(x, y, t), x), x))-0.4e-2*(diff(diff(w(x, y, t), y), y))+diff(diff(w(x, y, t), t), t)-w(x, y, t)-tau

 (3)
> 

BC := w(0, y, t) = 0, (D[1, 1](w))(0, y, t) = 0, w(a, y, t) = 0, (D[1, 1](w))(a, y, t) = 0, w(x, 0, t) = 0, (D[2, 2](w))(x, 0, t) = 0, w(x, b, t) = 0, (D[2, 2](w))(x, b, t) = 0

w(0, y, t) = 0, (D[1, 1](w))(0, y, t) = 0, w(a, y, t) = 0, (D[1, 1](w))(a, y, t) = 0, w(x, 0, t) = 0, (D[2, 2](w))(x, 0, t) = 0, w(x, b, t) = 0, (D[2, 2](w))(x, b, t) = 0

 (4)
> 

 

 

> 

BC1:=subs(a=1,b=1,[BC])

[w(0, y, t) = 0, (D[1, 1](w))(0, y, t) = 0, w(1, y, t) = 0, (D[1, 1](w))(1, y, t) = 0, w(x, 0, t) = 0, (D[2, 2](w))(x, 0, t) = 0, w(x, 1, t) = 0, (D[2, 2](w))(x, 1, t) = 0]

 (5)

We use the method of multiple scales to directly attack EOM1 and BC1. To transform the time derivatives in EOM1 in terms of the scales  and , we let

> 

timeScales:=T[0],T[1]

T[0], T[1]

 (6)
> 

dt[1]:=expr->add(epsilon^i*diff(expr,timeScales[i+1]),i=0..1)

proc (expr) options operator, arrow; add(epsilon^i*(diff(expr, timeScales[i+1])), i = 0 .. 1) end proc

 (7)
> 

msForm:={w(x,y,t)=w(x,y,timeScales),seq(diff(w(x,y,t),t$i)=dt[i](w(x,y,timeScales)),i=1..2)}

{diff(diff(w(x, y, t), t), t) = dt[2](w(x, y, T[0], T[1])), diff(w(x, y, t), t) = diff(w(x, y, T[0], T[1]), T[0])+epsilon*(diff(w(x, y, T[0], T[1]), T[1])), w(x, y, t) = w(x, y, T[0], T[1])}

 (8)
> 

multiScales:=`union`(map(s->subs(w=s,msForm),[w])[])

{diff(diff(w(x, y, t), t), t) = dt[2](w(x, y, T[0], T[1])), diff(w(x, y, t), t) = diff(w(x, y, T[0], T[1]), T[0])+epsilon*(diff(w(x, y, T[0], T[1]), T[1])), w(x, y, t) = w(x, y, T[0], T[1])}

 (9)

Then, we seek a second-order approximate solution in the form

> 

solRule:=w(x,y,timeScales)=add(epsilon^j*w[j](x,y,timeScales),j=1..3)

w(x, y, T[0], T[1]) = epsilon*w[1](x, y, T[0], T[1])+epsilon^2*w[2](x, y, T[0], T[1])+epsilon^3*w[3](x, y, T[0], T[1])

 (10)

We introduce the detuning  to describe the nearness of the edge lengths  and , consider the case of primary resonance, and hence let

> 

tau=epsilon^3*tau(x,y)*convert(cos(Omega*T[0]),exp)

tau = epsilon^3*tau(x, y)*((1/2)*exp(I*Omega*T[0])+(1/2)*exp(-I*Omega*T[0]))

 (11)
> 

lhs(EOM)

Error, invalid input: lhs received diff(diff(diff(diff(w(x, y, t), x), x), x), x)+.12*(diff(diff(diff(diff(w(x, y, t), x), x), y), y))+0.11e-2*(diff(diff(diff(diff(w(x, y, t), y), y), y), y))+10-.4*(diff(diff(w(x, y, t), x), x))-0.4e-2*(diff(diff(w(x, y, t), y), y))+diff(diff(w(x, y, t), t), t)-w(x, y, t)-tau, which is not valid for its 1st argument, expr

  

Substituting multiScales, solRule, and scaleRule2 into EOM1, expanding the result for small , and discarding terms of order higher than , we obtain

> 

expr83a:=seq(convert(series(value(subs(multiScales,solRule,lhs(EOM))),epsilon,4),polynom),i=1)

Error, invalid input: lhs received diff(diff(diff(diff(w(x, y, t), x), x), x), x)+.12*(diff(diff(diff(diff(w(x, y, t), x), x), y), y))+0.11e-2*(diff(diff(diff(diff(w(x, y, t), y), y), y), y))+10-.4*(diff(diff(w(x, y, t), x), x))-0.4e-2*(diff(diff(w(x, y, t), y), y))+diff(diff(w(x, y, t), t), t)-w(x, y, t)-tau, which is not valid for its 1st argument, expr

  

NULL

NULL

> 

t0 := time(); ST1_like := map(combine, select(has, select(has, ST, sin(m*Pi*x)), sin(n*Pi*y))); time_taken := time()-t0

.187

  

Error, incorrect number of extra arguments in select

  

0.

 (12)

``


 

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