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torabi

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These are replies submitted by torabi

@Carl Love  i do not know...only i...

torabi 85
December 18 2016
0 0

@Carl Love 

i do not know...only i  guess.

there is not any error...

torabi 85
November 30 2016
0 0

@taro 

i using maple 2016 and there is not any error!!!

for compare...

torabi 85
November 28 2016
0 0

@Preben Alsholm 

i want compare numerical solution with analytical solution...

 

is there another way?...

torabi 85
November 18 2016
0 1

@Preben Alsholm 

THANKS..is there another way for obtaining answer?

 

i use approx sol........

torabi 85
November 18 2016
0 0

@Preben Alsholm 

THANKS...i use approx sol in new maple code but i encounter with ''''

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging''''
also i use change of variable, but untill there is error'''

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {`1`, y}''''

please see it and help to me...

thanks

HAB2.mw

@Preben Alsholm  thanks...i can no...

torabi 85
November 16 2016
0 0

@Preben Alsholm 

thanks...i can not determine approx sol for it.

may i asked you for helping me?

 

how i can specify an approximate initial...

torabi 85
November 15 2016
0 0

@tomleslie 

thanks.i reform it again.but now there is another problem

''Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution''

how i can specify an approximate initial solution?

HAB1.mw

a similar code works correctly...

torabi 85
November 03 2016
0 0

@vv 

thanks..

i do not know, where is wrong?

please help me.also a similar code is attached, in which works correctly

please see it

AGM2.mw
 

> 

restart;
> 

u:=(sin(lambda*x)*(1+lambda*h*sin(lambda)))/(lambda*cos(lambda))+h*cos(lambda*x)-h-x;

sin(lambda*x)*(1+lambda*h*sin(lambda))/(lambda*cos(lambda))+h*cos(lambda*x)-h-x

 (1)
> 

d:=2.2e-05; omega:=1; h:=0.5/9; L:=9; m:=10; Ea:=2.23e+08; Omega:=0.0001;

0.22e-4

  

1

  

0.5555555556e-1

  

9

  

10

  

0.223e9

  

0.1e-3

 (2)
> 

lambda:=Omega*L*sqrt(m/Ea);

0.1905855975e-6

 (3)
> 

f:=sum(a[i]*x^i,i=0..5);

x^5*a[5]+x^4*a[4]+x^3*a[3]+x^2*a[2]+x*a[1]+a[0]

 (4)
> 

g:=sum(b[i]*x^i,i=0..5);

x^5*b[5]+x^4*b[4]+x^3*b[3]+x^2*b[2]+x*b[1]+b[0]

 (5)
> 

F:=(-f*omega^2-diff(u*diff(f,x),x)+d*diff(f,x$4))+(3/4)*(-(3/2)*diff(f,x$2)*(diff(f,x))^2-diff(diff(f,x)*diff(g,x),x))=0;

-a[5]*x^5-a[4]*x^4-a[3]*x^3-a[2]*x^2-a[1]*x-a[0]-(1.000000000*cos(0.1905855975e-6*x)-0.1058808875e-7*sin(0.1905855975e-6*x)-1)*(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])-(5246986.200*sin(0.1905855975e-6*x)+0.5555555556e-1*cos(0.1905855975e-6*x)-0.5555555556e-1-x)*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2])+0.2640e-2*x*a[5]+0.528e-3*a[4]-(9/8)*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2])*(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])^2-(3/4)*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2])*(5*x^4*b[5]+4*x^3*b[4]+3*x^2*b[3]+2*x*b[2]+b[1])-(3/4)*(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])*(20*x^3*b[5]+12*x^2*b[4]+6*x*b[3]+2*b[2]) = 0

 (6)
> 

G:=(-4/3)*(g*omega^2)-g*lambda^2-diff(g,x$2)-diff(f,x)*diff(f,x$2)=0;

-1.333333333*b[5]*x^5-1.333333333*b[4]*x^4-1.333333333*b[3]*x^3-1.333333333*b[2]*x^2-1.333333333*b[1]*x-1.333333333*b[0]-20*x^3*b[5]-12*x^2*b[4]-6*x*b[3]-2*b[2]-(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2]) = 0

 (7)
> 

f:=unapply(f,x);

proc (x) options operator, arrow; x^5*a[5]+x^4*a[4]+x^3*a[3]+x^2*a[2]+x*a[1]+a[0] end proc

 (8)
> 

g:=unapply(g,x);

proc (x) options operator, arrow; x^5*b[5]+x^4*b[4]+x^3*b[3]+x^2*b[2]+x*b[1]+b[0] end proc

 (9)
> 

F:=unapply(F,x);

proc (x) options operator, arrow; -x^5*a[5]-x^4*a[4]-x^3*a[3]-x^2*a[2]-x*a[1]-a[0]-(1.000000000*cos(0.1905855975e-6*x)-0.1058808875e-7*sin(0.1905855975e-6*x)-1)*(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])-(5246986.200*sin(0.1905855975e-6*x)+0.5555555556e-1*cos(0.1905855975e-6*x)-0.5555555556e-1-x)*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2])+0.2640e-2*x*a[5]+0.528e-3*a[4]-(9/8)*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2])*(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])^2-(3/4)*(20*x^3*a[5]+12*x^2*a[4]+6*x*a[3]+2*a[2])*(5*x^4*b[5]+4*x^3*b[4]+3*x^2*b[3]+2*x*b[2]+b[1])-(3/4)*(5*x^4*a[5]+4*x^3*a[4]+3*x^2*a[3]+2*x*a[2]+a[1])*(20*x^3*b[5]+12*x^2*b[4]+6*x*b[3]+2*b[2]) = 0 end proc

 (10)
> 

G:=unapply(G,x):
> 

s1:=f(0)=0;

a[0] = 0

 (11)
> 

s2:=g(0)=0;

b[0] = 0

 (12)
> 

s3:=D(f)(0)=.001;
#Changed for having non-zero f
> 

 

a[1] = 0.1e-2

 (13)
> 

s4:=D(D(f))(1)=0;

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

 (14)
> 

s5:=D(D(D(f)))(1)=0;

60*a[5]+24*a[4]+6*a[3] = 0

 (15)
> 

s6:=D(g)(1)=-0.5;
#By assuming we have first order derivative of f in 1
> 

 

5*b[5]+4*b[4]+3*b[3]+2*b[2]+b[1] = -.5

 (16)
> 

s7:=F(0);

-a[0]+0.528e-3*a[4]-(9/4)*a[2]*a[1]^2-(3/2)*a[2]*b[1]-(3/2)*a[1]*b[2] = 0

 (17)
> 

s8:=G(0);

-1.333333333*b[0]-2*b[2]-2*a[1]*a[2] = 0

 (18)
> 

s9:=F(1);

-.997360*a[5]-.999472*a[4]-a[3]-a[2]-a[1]-a[0]-(9/8)*(20*a[5]+12*a[4]+6*a[3]+2*a[2])*(5*a[5]+4*a[4]+3*a[3]+2*a[2]+a[1])^2-(3/4)*(20*a[5]+12*a[4]+6*a[3]+2*a[2])*(5*b[5]+4*b[4]+3*b[3]+2*b[2]+b[1])-(3/4)*(5*a[5]+4*a[4]+3*a[3]+2*a[2]+a[1])*(20*b[5]+12*b[4]+6*b[3]+2*b[2]) = 0

 (19)
> 

s10:=G(1);

-21.33333333*b[5]-13.33333333*b[4]-7.333333333*b[3]-3.333333333*b[2]-1.333333333*b[1]-1.333333333*b[0]-(5*a[5]+4*a[4]+3*a[3]+2*a[2]+a[1])*(20*a[5]+12*a[4]+6*a[3]+2*a[2]) = 0

 (20)
> 

s11:=D(F)(0);

-1.*a[1]+0.2640e-2*a[5]-(27/4)*a[3]*a[1]^2-9*a[2]^2*a[1]-(9/2)*a[3]*b[1]-6*a[2]*b[2]-(9/2)*a[1]*b[3] = 0

 (21)
> 

s12:=D(G)(0);

-1.333333333*b[1]-6*b[3]-4*a[2]^2-6*a[1]*a[3] = 0

 (22)
> 

S:=fsolve([s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12],{a[0],a[1],a[2],a[3],a[4],a[5],b[0],b[1],b[2],b[3],b[4],b[5]});

{a[0] = 0., a[1] = 0.1000000000e-2, a[2] = 0.1596786199e-4, a[3] = -0.3073828978e-2, a[4] = 0.3065845047e-2, a[5] = -0.9189551209e-3, b[0] = 0., b[1] = 0.6758384265e-1, b[2] = -0.1596786199e-7, b[3] = -0.1501555804e-1, b[4] = -.6025430725, b[5] = .3775270307}

 (23)
> 

f(x):=eval(sum(a[i]*x^i,i=0..5),S);

-0.9189551209e-3*x^5+0.3065845047e-2*x^4-0.3073828978e-2*x^3+0.1596786199e-4*x^2+0.1000000000e-2*x

 (24)
> 

g(x):=eval(sum(b[i]*x^i,i=0..5),S);

.3775270307*x^5-.6025430725*x^4-0.1501555804e-1*x^3-0.1596786199e-7*x^2+0.6758384265e-1*x

 (25)
> 

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

 
> 

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

 
> 

``


 

Download AGM2.mw

 

 

@Preben Alsholm  thanks... as you...

torabi 85
October 31 2016
0 0

@Preben Alsholm 

thanks...

as you say when at least one term  has no g1 in it, Solutions for omega2 are heavily dependent on the value of b..

i want in this equations determined minimum of omega2.

if for example i choose b=10^-20 or smaller, then i can gain minimum of omega2?

thanks....

for me text file with name '''txtop1.txt...

torabi 85
October 06 2016
0 0

@tomleslie 

for me text file with name '''txtop1.txt"''  do not create?

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

``

fy := eval(y(x), dsol5):

NULL



Download Numerical.mw

 

really thanks Dear prof Preben Alsholm...

torabi 85
October 01 2016
0 1

@Preben Alsholm 

really thanks Dear prof Preben Alsholm

what is the name of this numerical meth...

torabi 85
September 26 2016
0 0

@Mariusz Iwaniuk 

please tell me about the name of this numerical method for inverse  Laplace Transform?

for example a reference for it to write  algorithm?

thanks

NLaplace := proc (F, t, n, shift) local m, theta, z, dz; description "Inverse Laplace Transform"; m := 2*Pi/n; theta := -Pi+(s+1/2)*m; z := shift+n*(.5017*theta*cot(.6407*theta)-.6122+.2645*I*theta)/t; dz := n*((-1)*.5017*.6407*theta*csc(.6407*theta)^2+.5017*cot(.6407*theta)+.2645*I)/t; Re(evalf(-((1/2)*I)*m*(sum(exp(z*t)*F(z)*dz, s = 0 .. n))/Pi)) end proc

"Inverse Laplace Transform" ?...

torabi 85
September 26 2016
0 0

@Preben Alsholm 

thanks alot

how we can perform  "Inverse Laplace Transform" ?

please description it in maple?

@Mariusz Iwaniuk  Thanks alot why&n...

torabi 85
September 25 2016
0 1

@Mariusz Iwaniuk 

Thanks alot

why This method is not perfect?please explain

why in maple :` Solution. Maple can't inverse.`???is this problem relate  to this equation?

if this code is different for alpha=1/2 ?

what is F?

thanks

i want answer for Upsilon=1/2...

torabi 85
September 21 2016
0 0

 

 

 

is there answer for this case?

thanks

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