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how I can dsolve this differential equat...

torabi 90 Maple 2017
parameter dsolve
August 14 2017
2 10

hi...

how I can dsolve this differential equations. parameter p is unkown.

I want to gain w(x) and u(x) and psi(x) and p.

thanks

sade.mw
 

> 

restart; eq1 := (diff(psi(x), x))^2+(diff(u(x), x)+(8*(1/2))*(diff(w(x), x))^2)((diff(psi(x), x))^2)+3*(diff(w(x), x, x))+5*(diff(w(x), x, x))*(diff(psi(x), x))-7*(diff(u(x), x, x, x)+(8*(1/2))*(diff(w(x), x, x))^2+(3/2)*(diff(w(x), x, x, x))*(diff(w(x), x)))+3 = p

(diff(psi(x), x))^2+(diff(u(x), x))((diff(psi(x), x))^2)+4*(diff(w(x), x))((diff(psi(x), x))^2)^2+3*(diff(diff(w(x), x), x))+5*(diff(diff(w(x), x), x))*(diff(psi(x), x))-7*(diff(diff(diff(u(x), x), x), x))-28*(diff(diff(w(x), x), x))^2-(21/2)*(diff(diff(diff(w(x), x), x), x))*(diff(w(x), x))+3 = p

 (1)
> 

eq2 := (51-31)(diff(psi(x), x, x))+(52-2)(diff(w(x), x, x, x))+8*(diff(psi(x), x, x, x, x))-7*(diff(w(x), x)-psi(x)) = 0

70+8*(diff(diff(diff(diff(psi(x), x), x), x), x))-7*(diff(w(x), x))+7*psi(x) = 0

 (2)
> 

eq3 := 4*(diff(w(x), x, x)-(diff(psi(x), x)))+(23+11)(diff(psi(x), x, x, x))+(14+12)*(diff(w(x), x, x, x, x)) = 0

4*(diff(diff(w(x), x), x))-4*(diff(psi(x), x))+34+26*(diff(diff(diff(diff(w(x), x), x), x), x)) = 0

 (3)
> 

dsys3 := {eq1, eq2, eq3, psi(0) = 0, psi(1) = 0, u(0) = 0, u(1) = 0, w(0) = 0, w(1) = 0, ((D@@1)(psi))(0) = 0, ((D@@1)(psi))(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 12, got 10

  
> 

dsolve({eq2, eq3}, {psi(x), w(x)}):
> 

with(PDEtools, casesplit, declare);

[casesplit, declare]

 (4)
> 

 


 

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why this equation does not any answer?...

torabi 90 Maple 2016
dsolve
January 06 2017
0 3

hi

why this equation does not any answer?

thanks

s-s.mw
 

> 

restart
> 

``
> 

eq:={-J*g[1]*(diff(w(x), x, x, x, x, x, x))+J*c[1]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))+(beta[11]*A*0)*`ΔT`*(diff(w(x), x, x))+2*b*f[1133]*(Pi/L)^2*(d[33]*lambda[3]*`ΔT`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`ΔT`*L)*sin(Pi*x/L)*sinh(h*Pi/(2*L))/(2*cosh(h*Pi/(2*L))*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}

{-J*g[1]*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+J*c[1]*(diff(diff(diff(diff(w(x), x), x), x), x))+A*g[113113]*(diff(diff(diff(diff(w(x), x), x), x), x))+b*f[1133]*Pi^2*(d[33]*lambda[3]*`ΔT`*L/mu[33]-2*f[1133]*a*Pi/L-P[3]*`ΔT`*L)*sin(Pi*x/L)*sinh((1/2)*h*Pi/L)/(L^2*cosh((1/2)*h*Pi/L)*(-a33+d[33]^2/mu[33])) = 0, w(0) = 0, w(L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, ((D@@3)(w))(0) = 0, ((D@@3)(w))(L) = 0}

 (1)
> 

dsolve(eq, w(x))
> 

``


 

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Error, (in dsolve/numeric/BVPSolve) sing...

torabi 90 Maple 2016
dsolve numeric bvp
December 28 2016
0 6

hi.

how i can dsolve this differential equations?

thanks

ich.mw
 

restart; Digits := 50; dsol1 := dsolve({diff(F(eta), eta, eta, eta)+.5*H(eta)*((diff(F(eta), eta))^2+F(eta)*(diff(F(eta), eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(F(eta), eta, eta))/G(eta)-(diff(H(eta), eta))*(diff(F(eta), eta, eta))/H(eta) = 0, diff(G(eta), eta, eta)+H(eta)*((diff(F(eta), eta))*G(eta)+.5*F(eta)*(diff(eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))^2/G(eta)-((diff(H(eta), eta))*(diff(H(eta), eta)))/H(eta)+(diff(F(eta), eta, eta))^2-(H(eta)/G(eta))^2 = 0, diff(H(eta), eta, eta)+(.5*1.3)*H(eta)*(5*(diff(F(eta), eta))*H(eta)+F(eta)*(diff(H(eta), eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(H(eta), eta))/G(eta)-(diff(H(eta), eta))^2/H(eta)+(1.3*1.44)*H(eta)*(diff(F(eta), eta, eta))/G(eta)-(1.3*1.92)*(H(eta)/G(eta))^3 = 0, F(0) = 0, G(0) = 0, H(0) = 0, (D(F))(0) = 1, (D(F))(1) = 0, (D(G))(0) = 0, (D(H))(0) = 0}, 'maxmesh' = 900, numeric, output = listprocedure, method = bvp[middefer], abserr = 0.1e-2); fy := eval(F(eta), dsol1)

Error, invalid input: eval received dsol1, which is not valid for its 2nd argument, eqns

  

 

NULL


 

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how i can solve or fsolve this equations...

torabi 90 Maple 2016
solve fsolve
December 18 2016
1 2

hi.how i can solve or fsolve this equations?

i can not with fsolve?

thanks alot

SOLVE.mw


Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/SOLVE.mw .
 

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error message'' which is not valid for i...

torabi 90 Maple 2016
syntax
December 03 2016
1 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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