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@dharr  Is there no way to solve it...

arshl 15
July 26 2019
0 0

@dharr  Is there no way to solve it with Maple?

@dharr  Hi.   ...

arshl 15
July 26 2019
0 0

@dharr  Hi.
 

> 

``
> 

equation is:"(∂)/(∂ t)u=(∂)/(∂ x)(u(∂u)/(∂ x))+u(1-u) x>=0, t>=0"``

Error, missing operator or `;`

  

 

> 

restart
> 

with(inttrans)
> 

pde := diff(u(x, t), t) = u(x, t)*(diff(u(x, t), `$`(x, 2)))+(diff(u(x, t), x))^2+u(x, t)-u(x, t)^2

diff(u(x, t), t) = u(x, t)*(diff(diff(u(x, t), x), x))+(diff(u(x, t), x))^2+u(x, t)-u(x, t)^2

 (1)
> 

laplace(pde, x, s); collect(subs(laplace(u(x, t), x, s) = U(t), %), s); Lpde := eval(%, s = I*omega)

diff(laplace(u(x, t), x, s), t) = laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s)+laplace((diff(u(x, t), x))^2, x, s)+laplace(u(x, t), x, s)-laplace(u(x, t)^2, x, s)

  

diff(U(t), t) = laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s)+laplace((diff(u(x, t), x))^2, x, s)+U(t)-laplace(u(x, t)^2, x, s)

  

diff(U(t), t) = eval(laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s), {s = I*omega})+eval(laplace((diff(u(x, t), x))^2, x, s), {s = I*omega})+U(t)-(eval(laplace(u(x, t)^2, x, s), {s = I*omega}))

 (2)

condition: u(x,0)=1-exp(-(1/2)*x*sqrt(2)),    u(0,t)=1-exp(-(1/2)*t),    u[x](0, t) = (1/2)*sqrt(2)*exp(-(1/2)*t)

1-exp(-(1/2)*x*2^(1/2))

  

1-exp(-(1/2)*t)

 (3)
> 

ic := u(x, 0) = 1-exp(-x/sqrt(2)); bc1 := u(0, t) = 1-exp(-(1/2)*t); bc2 := (D[1](u))(0, t) = exp(-(1/2)*t)/sqrt(2)

u(x, 0) = 1-exp(-(1/2)*x*2^(1/2))

  

u(0, t) = 1-exp(-(1/2)*t)

  

(D[1](u))(0, t) = (1/2)*2^(1/2)*exp(-(1/2)*t)

 (4)
> 

eval(Lpde, {bc1, bc2})

diff(U(t), t) = eval(laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s), {s = I*omega})+eval(laplace((diff(u(x, t), x))^2, x, s), {s = I*omega})+U(t)-(eval(laplace(u(x, t)^2, x, s), {s = I*omega}))

 (5)
> 

fourier(ic, x, omega); subs(fourier(u(x, 0), x, omega) = U(0), %)

fourier(u(x, 0), x, omega) = 2*Pi*Dirac(omega)-fourier(exp(-(1/2)*x*2^(1/2)), x, omega)

  

U(0) = 2*Pi*Dirac(omega)-fourier(exp(-(1/2)*x*2^(1/2)), x, omega)

 (6)

Desired output is: U
diff(U, t)+(1+(1/2)*omega^2)*U^2+e^(-(1/2)*t)*(1-e^(-(1/2)*t))/sqrt(2)+(1/2)*i*omega*(1-e^(-(1/2)*t))^2 = 0
U(omega,0)=πδ(omega)
-i*sqrt(2)*U*is*fourier*transform*of*u/omega(2*`iω`+sqrt(2))

omega

  

omega

  

-i*2^(1/2)*U*is*fourier*transform*of*u/omega(2*`iω`+2^(1/2))

 (7)
> 

``

 

 


 

Download Case1.mw
 

> 

``
> 

equation is:"(∂)/(∂ t)u=(∂)/(∂ x)(u(∂u)/(∂ x))+u(1-u) x>=0, t>=0"``

Error, missing operator or `;`

  

 

> 

restart
> 

with(inttrans)
> 

pde := diff(u(x, t), t) = u(x, t)*(diff(u(x, t), `$`(x, 2)))+(diff(u(x, t), x))^2+u(x, t)-u(x, t)^2

diff(u(x, t), t) = u(x, t)*(diff(diff(u(x, t), x), x))+(diff(u(x, t), x))^2+u(x, t)-u(x, t)^2

 (1)
> 

laplace(pde, x, s); collect(subs(laplace(u(x, t), x, s) = U(t), %), s); Lpde := eval(%, s = I*omega)

diff(laplace(u(x, t), x, s), t) = laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s)+laplace((diff(u(x, t), x))^2, x, s)+laplace(u(x, t), x, s)-laplace(u(x, t)^2, x, s)

  

diff(U(t), t) = laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s)+laplace((diff(u(x, t), x))^2, x, s)+U(t)-laplace(u(x, t)^2, x, s)

  

diff(U(t), t) = eval(laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s), {s = I*omega})+eval(laplace((diff(u(x, t), x))^2, x, s), {s = I*omega})+U(t)-(eval(laplace(u(x, t)^2, x, s), {s = I*omega}))

 (2)

condition: u(x,0)=1-exp(-(1/2)*x*sqrt(2)),    u(0,t)=1-exp(-(1/2)*t),    u[x](0, t) = (1/2)*sqrt(2)*exp(-(1/2)*t)

1-exp(-(1/2)*x*2^(1/2))

  

1-exp(-(1/2)*t)

 (3)
> 

ic := u(x, 0) = 1-exp(-x/sqrt(2)); bc1 := u(0, t) = 1-exp(-(1/2)*t); bc2 := (D[1](u))(0, t) = exp(-(1/2)*t)/sqrt(2)

u(x, 0) = 1-exp(-(1/2)*x*2^(1/2))

  

u(0, t) = 1-exp(-(1/2)*t)

  

(D[1](u))(0, t) = (1/2)*2^(1/2)*exp(-(1/2)*t)

 (4)
> 

eval(Lpde, {bc1, bc2})

diff(U(t), t) = eval(laplace(u(x, t)*(diff(diff(u(x, t), x), x)), x, s), {s = I*omega})+eval(laplace((diff(u(x, t), x))^2, x, s), {s = I*omega})+U(t)-(eval(laplace(u(x, t)^2, x, s), {s = I*omega}))

 (5)
> 

fourier(ic, x, omega); subs(fourier(u(x, 0), x, omega) = U(0), %)

fourier(u(x, 0), x, omega) = 2*Pi*Dirac(omega)-fourier(exp(-(1/2)*x*2^(1/2)), x, omega)

  

U(0) = 2*Pi*Dirac(omega)-fourier(exp(-(1/2)*x*2^(1/2)), x, omega)

 (6)

Desired output is: U
diff(U, t)+(1+(1/2)*omega^2)*U^2+e^(-(1/2)*t)*(1-e^(-(1/2)*t))/sqrt(2)+(1/2)*i*omega*(1-e^(-(1/2)*t))^2 = 0
U(omega,0)=πδ(omega)
-i*sqrt(2)*U*is*fourier*transform*of*u/omega(2*`iω`+sqrt(2))

omega

  

omega

  

-i*2^(1/2)*U*is*fourier*transform*of*u/omega(2*`iω`+2^(1/2))

 (7)
> 

``

 

 


 

Download Case1.mw

 

Why not get the correct answer for the equation below?

@Rouben Rostamian   Thank you for y...

arshl 15
July 26 2019
0 0

@Rouben Rostamian   Thank you for your all your help

new question...

arshl 15
July 25 2019
0 0

@Rouben Rostamian  You helped me earlier. Can you help Fourier transforms partial differential equations with initial and boundry condition? the equation and the it;s Fourier transform are in following. thanks alot

> 

restart
> 

pde := diff(u(x, t), t)+diff(u(x, t), `$`(x, 2))+u(x, t)-exp(-x*(1+2*t)) = 0

diff(u(x, t), t)+diff(diff(u(x, t), x), x)+u(x, t)-exp(-x*(1+2*t)) = 0

 (1)

condition: u(x,0)=x,    u(0,t)=t,    u[x](0, t) = e^(-t)-t

> 

x >= 0

0 <= x

 (2)
> 

t >= 0

0 <= t

 (3)
> 

``

I want to get this equation: "(&PartialD;)/(&PartialD; t)u^(~)+u^(~)-e^(-t)+t-iomegat-omega^(2)u^(~)-((1+2 t)/(1+iomega))=0,"

`#msup(mi("u",fontweight = "bold",mathcolor = "red"),mo("&tilde;",fontweight = "bold",mathcolor = "red"))`(omega,0)=i(i+omega^2π(D(delta))(omega))/omega^2

`#msup(mi("u",fontweight = "bold",mathcolor = "red"),mo("&tilde;",fontweight = "bold",mathcolor = "red"))` id fourier transform of u

> 

``

 


 

Download equationF.mw

Thanks...

arshl 15
July 25 2019
0 0

@dharr Thank you

@nm  Because I wanted to show the e...

arshl 15
July 24 2019
0 0

@nm  Because I wanted to show the equation and the answer I want to make
 

> 

restart
> 

pde := diff(u(x, t), t)+diff(u(x, t), `$`(x, 2))+u(x, t)-exp(-x*(1+2*t)) = 0

diff(u(x, t), t)+diff(diff(u(x, t), x), x)+u(x, t)-exp(-x*(1+2*t)) = 0

 (1)

condition: u(x,0)=x,    u(0,t)=t,    u[x](0, t) = e^(-t)-t

> 

x >= 0

0 <= x

 (2)
> 

t >= 0

0 <= t

 (3)
> 

``

I want to get this equation: "(&PartialD;)/(&PartialD; t)u^(~)+u^(~)-e^(-t)+t-iomegat-omega^(2)u^(~)-((1+2 t)/(1+iomega))=0,"

`#msup(mi("u",fontweight = "bold",mathcolor = "red"),mo("&tilde;",fontweight = "bold",mathcolor = "red"))`(omega,0)=i(i+omega^2π(D(delta))(omega))/omega^2

`#msup(mi("u",fontweight = "bold",mathcolor = "red"),mo("&tilde;",fontweight = "bold",mathcolor = "red"))` id fourier transform of u

> 

``

 


 

Download equationF.mw

@Rouben Rostamian   I encountered a...

arshl 15
June 29 2019
0 0

@Rouben Rostamian   I encountered a problem. If the m1 changes to

m1 := (1/2)*b11*ro*Pi*R^2*exp(-my*cp1/(R*p1))*(my*cp2/(R*p1)-cp3)/p1;

 

, Maple can not integrate againcorrected2.mw

@Rouben Rostamian  thank you so muc...

arshl 15
June 27 2019
0 0

@Rouben Rostamian  thank you so much

 

@Rouben Rostamian   Thank you so mu...

arshl 15
June 26 2019
0 0

@Rouben Rostamian   Thank you so much . But a question.

for example in fact v[2] is a function of time and p1.  not defining it as a function of time and p1 does not create  problem? and do not need to be expressed as a function of time and p1 in the following command?
 

dsolve({g, v[3](20)=0}, v[3](t));

for example dsolve({g, v[3](p1,20)=0}, v[3](t));

thank you

@Rouben Rostamian   Oh, sorry, I f...

arshl 15
June 25 2019
0 0

@Rouben Rostamian  

Oh, sorry, I forgot save Pi istead pi in sendenig file. m1(p1, my(t))  It is a part of my differential equation that is defined for simplicity separately as m1 that  which itself is a function of p1 and my(t). Thanks

code...

arshl 15
June 25 2019
0 0

@Rouben Rostamian  maplequ.mw

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