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dsolve nonlinear differential equations...

torabi 90 Maple 2016
dsolve nonlinear numeric
November 14 2016
0 8

HI

please help me for dsolve this nonlinear differential equations

thanls...

HAB.mw
 

restart; Digite := 100; Phi0 := 5; A := b*h; g13 := 31/250000000; g1 := 113/500000; f13 := 1/1000000000; c1 := 226000000000000; b := 10*10^(-9); J := (1/12)*b*h^3; h := 15*10^(-9); L := 100*10^(-9); E1 := (339/10000000000000000000000)*(diff(u(x), x, x, x, x))+(1017/10000000000000000000000)*(diff(w(x), x, x))*(diff(w(x), x, x, x))+(339/10000000000000000000000)*(diff(w(x), x, x, x, x))*(diff(w(x), x))-(339/10000)*(diff(u(x), x, x))-(339/10000)*(diff(w(x), x))*(diff(w(x), x, x)) = 0

E2 := -(1017/1600000000000000000000000000000000000000)*(diff(w(x), x, x, x, x, x, x))+(1589109/2500000000000000000000000)*(diff(w(x), x, x, x, x))-(339/10000*(diff(u(x), x, x)+(diff(w(x), x))*(diff(w(x), x, x))))*(diff(w(x), x))-(diff(w(x), x, x))*((339/10000)*(diff(u(x), x))+(339/20000)*(diff(w(x), x))^2+0.5824000000e-4)+(339/10000000000000000000000)*(diff(w(x), x, x))*(diff(u(x), x, x, x)+(diff(w(x), x, x))^2+(diff(w(x), x, x, x))*(diff(w(x), x)))+(339/10000000000000000000000)*(diff(w(x), x))*(diff(u(x), x, x, x, x)+3*(diff(w(x), x, x))*(diff(w(x), x, x, x))+(diff(w(x), x, x, x, x))*(diff(w(x), x)))-2 = 0:
 

E3 := -5.385803274*10^(-17)*(diff(Phi(x), x, x))+2.659881780*Phi(x)-5.125107476*10^(-20)*(diff(psi(x), x, x))+1.146681319*psi(x)+3.300000000*10^(-8)*(diff(w(x), x, x)) = 0:

E4 := -5.125107476*10^(-20)*(diff(Phi(x), x, x))+1.146681319*Phi(x)+(891/100000000000000)*(diff(psi(x), x, x))/Pi+34976.39822*psi(x)+0.4351500000e-5*(diff(w(x), x, x)) = 0:

dsys3 := {EQ1, EQ2, EQ3, EQ4, c1*J*((D@@2)(w))(0)+A*g13*((D@@2)(w))(0)-2*b*f13*Phi0-g1*J*((D@@4)(w))(0)+g1*A*(((D@@2)(u))(0)+((D@@1)(w))(0)*((D@@2)(w))(0))*((D@@1)(w))(0) = 0, c1*J*((D@@2)(w))(L)+A*g13*((D@@2)(w))(L)-2*b*f13*Phi0-g1*J*((D@@4)(w))(L)+g1*A*(((D@@2)(u))(L)+((D@@1)(w))(L)*((D@@2)(w))(L))*((D@@1)(w))(L) = 0, Phi(0) = 0, Phi(L) = 0, psi(0) = 0, psi(L) = 0, u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0}; dsolve(dsys3, numeric, initmesh = 3024, abserr = 0.1e-4)

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

  

``


 

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a problem with fsolve...

torabi 90 Maple 2016
fsolve
November 03 2016
1 2

hi

please help me for fsolve algebric equations...

thanks

AGM.mw
 

> 

restart:
> 

F(eta):=sum(a[i]*eta^i,i=0..5):
> 

theta(eta):=sum(b[i]*eta^i,i=0..5):K(eta):=sum(c[i]*eta^i,i=0..5):Omega(eta):=sum(d[i]*eta^i,i=0..5):
> 

``
> 

U1:=diff(theta(eta), eta, eta)-3*Omega(eta)*(F(eta)*(diff(theta(eta), eta))-theta(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(theta(eta), eta)) = 0:U2:= diff(F(eta), eta, eta, eta)+Omega(eta)*(3*F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2)/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(F(eta), eta, eta))+Omega(eta)/K(eta) = 0:U3:= diff(K(eta), eta, eta)+Omega(eta)*(1.5*F(eta)*(diff(K(eta), eta))-K(eta)*(diff(F(eta), eta)))/K(eta)+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(K(eta), eta))+(diff(F(eta), eta, eta))^2-Omega(eta)^2 = 0:U4:= diff(Omega(eta), eta, eta)+Omega(eta)*(3*F(eta)*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta, eta))^2/K(eta)-Omega(eta)^3/K(eta) = 0:
> 

F(eta):=unapply(F(eta),eta):
> 

theta(eta):=unapply(theta(eta),eta):K(eta):=unapply(K(eta),eta):Omega(eta):=unapply(Omega(eta),eta):
> 

U1:=unapply(U1,eta):U2:=unapply(U2,eta):U3:=unapply(U3,eta):U4:=unapply(U4,eta):
> 

 

> 

s1:=F(eta)(0) = 0:
> 

s2:=K(eta)(0) = 0:s3:=Omega(eta)(0) = 0:s4:=theta(eta)(0) = 1:s5:=theta(eta)(1) = 0:s6:=(D(F(eta)))(0) = 0:s7:=(D(K(eta)))(1) = 0:s8:=(D(Omega(eta)))(1) = 0:s9:=((D@@2)(F(eta)))(1) = 0

20*a[5]+12*a[4]+6*a[3]+2*a[2] = 0

 (1)
> 

s10:=U1(0):s11:=U2(0):s12:=U3(0):s13:=U4(0):        s14:=U1(1):s15:=U2(1):s16:=U3(1):s17:=U4(1):    s18:=D(U1)(0):s19:=D(U2)(0):s20:=D(U3)(0):s21:=D(U4)(0):     s22:=D(U1)(1):s23:=D(U2)(1):s24:=D(U3)(1):
> 

 

> 

 

> 

Q:=fsolve([s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13,s14,s15,s16,s17,s18,s19,s20,s21,s22,s23,s24],{a[0],a[1],a[2],a[3],a[4],a[5],b[0],b[1],b[2],b[3],b[4],b[5],c[0],c[1],c[2],c[3],c[4],c[5],d[0],d[1],d[2],d[3],d[4],d[5]}):
> 

F(eta):=eval(sum(a[i]*eta^i,i=0..5),Q):

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

  
> 

theta(eta):=eval(sum(b[i]*eta^i,i=0..5),Q):K(eta):=eval(sum(c[i]*eta^i,i=0..5),Q):Omega(eta):=eval(sum(d[i]*eta^i,i=0..5),Q):

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

  
> 

plot(g(x),x=0..1,axes=boxed,color=green,thickness=2,labels=[x,g]):

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

  
> 

plot(f(x),x=0..1,axes=boxed,color=blue,thickness=2,labels=[x,f]):

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

  
> 

 


 

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is correct this answer for differential ...

torabi 90 Maple 2016
dsolve
October 30 2016
1 2

hi..

is correct this answer for differential equations??

i think order of result should be in (10^6 or 10^9 or higher) range....

please check it

thanks

hpp.mw
 

> 

restart
> 

L := 100*10^(-9):
> 

Eq1 := {-(1017/1600000000000000000000000000000000000000000)*(diff(w(x), x, x, x, x, x, x))+(26169/40000000000000000000000000)*(diff(w(x), x, x, x, x))-0.8325000000e-4*omega^2+1.560937500*10^(-21)*omega^2*(diff(w(x), x, x)), w(0) = 0, w(1/10000000) = 0, (D(w))(0) = 0, (D(w))(1/10000000) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(1/10000000) = 0}:
> 

sys := subs(omega^2 = omega2, Eq1);

{-(1017/1600000000000000000000000000000000000000000)*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+(26169/40000000000000000000000000)*(diff(diff(diff(diff(w(x), x), x), x), x))-0.8325000000e-4*omega2+0.1560937500e-20*omega2*(diff(diff(w(x), x), x)), w(0) = 0, w(1/10000000) = 0, (D(w))(0) = 0, (D(w))(1/10000000) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(1/10000000) = 0}

  

{-(5085/8)*(diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y))+6542250*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.8325000000e-4*omega2+0.1560937500e-6*omega2*(diff(diff(g1(y), y), y)), 10000000*(D(g1))(0) = 0, 10000000*(D(g1))(1) = 0, 100000000000000*((D@@2)(g1))(0) = 0, 100000000000000*((D@@2)(g1))(1) = 0, g1(0) = 0, g1(1) = 0}

  

{-(5085/8)*(diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y))+6542250*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.8325000000e-4*omega2+0.1560937500e-6*omega2*(diff(diff(g1(y), y), y))}, {10000000*(D(g1))(0) = 0, 10000000*(D(g1))(1) = 0, 100000000000000*((D@@2)(g1))(0) = 0, 100000000000000*((D@@2)(g1))(1) = 0, g1(0) = 0, g1(1) = 0}

  

{g1(0) = 0, g1(1) = 0, (D(g1))(0) = 0, (D(g1))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0}

  

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y), diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), diff(diff(diff(diff(g1(y), y), y), y), y), diff(diff(diff(g1(y), y), y), y), diff(diff(g1(y), y), y), diff(g1(y), y)}

  

{-(1017/1600000000000000000000000000000000000000000)*(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))+(26169/40000000000000000000000000)*(diff(diff(diff(diff(w(x), x), x), x), x))-0.8325000000e-4*omega2+0.1560937500e-20*omega2*(diff(diff(w(x), x), x))}

  

{-(5085/8)*(diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y))+6542250*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.8325000000e-4*omega2+0.1560937500e-6*omega2*(diff(diff(g1(y), y), y))}

  

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y) = 10292.62537*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.1309734513e-6*omega2+0.2455752212e-9*omega2*(diff(diff(g1(y), y), y))}

  

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y) = 10292.62537*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.1309734513e13*omega3+2455752212.*omega3*(diff(diff(g1(y), y), y))}

  

{diff(diff(diff(diff(diff(diff(g1(y), y), y), y), y), y), y) = 10292.62537*(diff(diff(diff(diff(g1(y), y), y), y), y))-0.1309734513e13*omega3+2455752212.*omega3*(diff(diff(g1(y), y), y)), g1(0) = 0, g1(1) = 0, (D(g1))(0) = 0, (D(g1))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0}

  

{((D@@3)(g1))(0), ((D@@3)(g1))(1), ((D@@4)(g1))(0), ((D@@4)(g1))(1), ((D@@5)(g1))(0), ((D@@5)(g1))(1)}

  

((D@@3)(g1))(0)

  

((D@@3)(g1))(1)

  

((D@@4)(g1))(0)

  

((D@@4)(g1))(1)

  

((D@@5)(g1))(0)

  

((D@@5)(g1))(1)

  

((D@@5)(g1))(1), ((D@@4)(g1))(0), ((D@@5)(g1))(0), ((D@@3)(g1))(1), ((D@@4)(g1))(1), ((D@@3)(g1))(0)

  

HFloat(-8.852947665097804e-24), HFloat(-8.991820290300328e-22), HFloat(8.852947665097804e-24), HFloat(-9.672787782157173e-20), HFloat(-8.991820290300328e-22), HFloat(9.672787782157165e-20)

 (1)
> 

sqrt(8.85294766509780*10^(-21)*10^19);

.2975390338

 (2)
> 

NULL


 

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how i can save results in maple in text ...

torabi 90 Maple 2016
export save exportmatrix
October 06 2016
1 2

hi...

how i can save results in text file?

for example in attached code maple i want save results for different ''x'' and fy(x), wherer x is between 0 to 1 i.e. (0,fy(0)) , (0.1,fy(0.1)) ,(0.2,fy(0.2)),....

in text file two column should be create.one of them for ''x'' and the onther for ,fy(x)

thanks...

Numerical_.mw

restart; E := 0.169e12; mu := 0.658e11; hl2 := 4; D1 := 1; n := 3; `αn` := 0.; beta := 16.474184; xi := 1.5; lambda := .1; dsys5 := {D1*(diff(y(x), x, x, x, x)) = `αn`/(1-y(x))^n-beta*(lambda*cosh(xi*(1-y(x)))-1/2*(lambda^2+1))/sinh(xi*(1-y(x)))^2, y(0) = 0, (D(y))(0) = 0, ((D@@2)(y))(1) = 0, ((D@@3)(y))(1) = 0}; dsol5 := dsolve(dsys5, 'maxmesh' = 900, numeric, output = listprocedure); fy := eval(y(x), dsol5); fy(1)

HFloat(0.3189919226404612)

 (1)

NULL

NULL

NULL

NULL



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not answer found for dsolve??...

torabi 90 Maple 2015
dsolve
September 26 2016
1 6

hi

in attached file below not answer found for dsolve?

please help me

thanks..

dsove.mw

> 

restart
> 

J := 1:
> 

PDE := diff(T(z, t), z, z)-.2*(diff(T(z, t), t, t)) = int(.7703831837*(diff(T(z, tau), tau, tau))/(t-tau)^.3, tau = 0 .. t):
> 

with(inttrans):
> 

sol := laplace(PDE, t, s):
> 

> 

sol2 := subs([laplace(T(z, t), t, s) = U(z, t), T(z, 0) = sin(J*Pi*z), (D[2](T))(z, 0) = 0], sol)

diff(diff(U(z, t), z), z)-.2000000000*s^2*U(z, t)+.2000000000*s*sin(Pi*z) = -1.000000000*s^.3000000000*sin(Pi*z)+1.000000000*s^1.300000000*U(z, t)

 (1)
> 

> 

sol3 := dsolve([sol2, (D[1](U))(0, t) = 0, (D[1](U))(1, t) = 0], U(z, t))

"sol3 := "

 (2)
> 

U(z, t) = invlaplace(rhs(sol3), s, t)

Error, invalid input: rhs expects 1 argument, but received 0

  
> 

sol4 := simplify(subs(z = 0, rhs(sol3)))

Error, invalid input: rhs expects 1 argument, but received 0

  
> 

``
> 

``



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