lijiwei

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10 years, 291 days

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These are questions asked by lijiwei

I want to get numerical solution of the Eqs.ode(see the folowlling ode and ibc)in Maple.However,when i run the following procedure,it prompts an error "Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution". How to solve the issue? Please help me.


restart:
n := 1.4; phi := 1; beta := .6931; psi := 1

> restart;
> n := 1.4; phi := 1; beta := .6931; psi := 1;

> s := proc (x) options operator, arrow; evalf(1+(phi*exp(beta*psi)*h(x))^n) end proc;

> Y := proc (x) options operator, arrow; evalf(f-(1/2-(1/2)/n)*ln(s(x))+2*ln(1-(1-s(x))^(-1+1/n))) end proc;


> ode := diff(h(x), `$`(x, 2))+(diff(Y(x), x))*(diff(h(x), x)+1) = 0;


> ibc := h(0) = 0, ((D(h))(10)+1)*s(10)^(-(1-1/n)*(1/2))*(1-(1-1/s(10))^(1-1/n))^2 = 0;

> p := dsolve({ibc, ode}, numeric);
Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution
>

I want to invlaplace the following complex expression that I call PQ.

>PQ:=(cosh((1/2)*eta*sqrt(C3^2+4*C1*s))*sqrt(C3^2+4*C1*s)+sinh((1/2)*eta*sqrt(C3^2+4*C1*s))*C3)*(cosh((1/2)*eta*C3)-sinh((1/2)*eta*C3))*(-cosh(C4)-sinh(C4)+s)/(s^2*(-sinh((1/2)*C3)+cosh((1/2)*C3))*(sinh((1/2)*sqrt(C3^2+4*C1*s))*C3+sqrt(C3^2+4*C1*s)*cosh((1/2)*sqrt(C3^2+4*C1*s))))

where C1 C3 C4 eta are constant .

Then I do like this

>invlaplace(PQ)

But I got

Iwould like to calculate the inverse laplace transform of the expreesion which I call T.

< T:=tanh(s):

To do this I use the code "invlaplace" to solve it.

<invlaplace(T,s,t)

But it returns "invlaplace(tanh(s),s,t)".Done nothing.How to get its mathematical expression? I am really interested to get it.

PLZ help me in anyway as you can as I am completely stuck.

I would like to plot the following expression that I call W

>W:=tau*exp(C4)/C1-exp(C4)*(exp(C3-C3*eta)/C3^2-exp(C3)/C3^2+tau/C1+eta/C3)+exp(C4-C3*eta/2)*Sum(16*beta[m]*sin(beta[m]*eta/2)*exp(-(beta[m]*beta[m]+C3^2)*tau/(4*C1))/((beta[m]*beta[m]+C3^2)*( beta[m]*beta[m]-C3^2)^2),m=1..n)

Where C1, C3, C4 are constant, and  beta[m]satisfies the relationship  

C3*sin (beta/2) =beta*cos (beta/2)

I want to plot the W-eta curve and W-tau curve (eta at [0, 1...

I would like to solve the following equation that I call equ?

> equ: = tanh(s)=C3*s

To do this I use the code “solve” to solve it. C3 is constant.

> sol: =solve (equ,s)

RootOf(_Z*C3*(exp(_Z))^2+_Z*C3-(exp(_Z))^2+1)

I then get the RootOf expression. How to get its mathematical expressions? I am really interested in getting it.

Please help me in anyway you can as I am completely stuck

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