adel-00

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11 years, 258 days

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These are replies submitted by adel-00

@Ali Guzel  

it is run for 20 min then i stop , i think that is not work

@acer 

thanks 

do u mean explicit(solve(K1=0,R));

still no roots

@Rouben Rostamian  

The resean is to find the coefficients of the Expression 

as

CoefficientList(r, (D[1](Q))(x*H2(t), H3(t)))

@tomleslie 

I change the ics to be function of x.. that is error

@tomleslie 

Thank you for your help..

I made changes in the Ics

still i had an error

  restart:
assume(x, real); assume(t, real):
  sys:= { -diff(v(x,t),t)+0.5*p*diff(u(x,t),x,x)+q*u(x,t)*(u(x,t)^2+v(x,t)^2)=0,
           diff(u(x,t),t)+0.5*p*diff(v(x,t),x,x)+q*v(x,t)*(u(x,t)^2+v(x,t)^2)=0
        };
  bc:= u(0,t) = 2,
       v(0,t) = 0,
       u(1,t) = 0,  # made this up
       v(1,t) = 0;  # made this up
  ic := u(x,0) = 4.999999999*10^9*cosh(1.414213562*x)/(3.535533906*10^9*cosh(1.414213562*x)-5.000000000*10^9),
        v(x,0) = 0;
  pdsol := pdsolve(eval(sys, [p=1, q=0.5]), {ic, bc}, numeric);
  p1:= pdsol:-plot3d( u(x,t), x=0..1, t=0..5, color=red, style=surface, transparency=0.5):
  p2:= pdsol:-plot3d( v(x,t), x=0..1, t=0..5, color=blue, style=surface, transparency=0.5):
  plots:-display([p1,p2]);

{diff(u(x, t), t)+.5*p*(diff(diff(v(x, t), x), x))+q*v(x, t)*(u(x, t)^2+v(x, t)^2) = 0, -(diff(v(x, t), t))+.5*p*(diff(diff(u(x, t), x), x))+q*u(x, t)*(u(x, t)^2+v(x, t)^2) = 0}

 

u(0, t) = 2, v(0, t) = 0, u(1, t) = 0, v(1, t) = 0

 

u(x, 0) = 4999999999.*cosh(1.414213562*x)/(3535533906.*cosh(1.414213562*x)-5000000000.), v(x, 0) = 0

 

_m5028535360

 

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
Newton iteration is not converging

 

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
Newton iteration is not converging

 

Error, (in plots:-display) expecting plot structures but received: [p1, p2]

 

 

4999999999.*cosh(1.414213562*x)/(3535533906.*cosh(1.414213562*x)-5000000000.)

(1)

``

Download pdeProb-2.mw

pde_2022.mw

I dont know what is the error

@acer 

Many thanks

@dharr 

Many thanks

@Carl Love 

here the approximation is real

Yp  := k -> (y[k+1]-y[k-1])/2/((1+alpha)*GAMMA(1+alpha)*h^(alpha)):Ypp := k -> (y[k+1]-2*y[k]+y[k-1])/((2-alpha)*GAMMA(2-alpha)*(h^(2-alpha))^2):

 

@Carl Love 

yes you are right but what can i do maybe there is somthing to do with sequence or the loop

or k from 1 to N-1 do
eq[k] := eval( ode1,
                    {x=X(k), y(x)=y[k],
                     diff(y(x),x)=Yp(k),
                     diff(y(x),x$2)=Ypp(k)} ):
    end do:

@mmcdara 

thank you very much

n(t) is real

  • Do you want to plot n(t) versus t for a countable set of delta values in 3D-like representation (a solution is given below)? Yes this is the case
  •  

@mmcdara 

Thanks for all the comments

 how we can plot 3d of n(t) agianst t and delta

restart:
assume(t,real):
a:=1:alpha:=1.2:h:=0.1:b:=GAMMA(2-alpha)/((1-alpha)*GAMMA(1-alpha)):
for n from 0 to 10 do
x[n]:=n*h:
vo[n]:=a*(x[n]-b*(ln((x[n]+b)/b))):
uo[n]:=a*(t-b*(ln((t+b)/b))):
u1[n]:=evalf(Int((x[n]-t)^(-alpha)*uo[n],t=0..x[n])):
S[n]:=vo[n]+u1[n]:
od:

data:=[seq([x[n],S[n]],n=0..10)]:
plot(data,axes=boxed);

@Carl Love 

Thanks 

       /x                   / 
      |                     | 
      |          (-alpha)   | 
J :=  |   (x - t)         a |t
     /                      \ 
      0                       

                        /    t (1 - alpha) GAMMA(1 - alpha)\\   
     GAMMA(2 - alpha) ln|1 + ------------------------------||   
                        \           GAMMA(2 - alpha)       /|   
   - -------------------------------------------------------| dt
                  (1 - alpha) GAMMA(1 - alpha)              /   
           1             /  / (-alpha)        /
------------------------ |a |x         MeijerG|
(-1 + alpha) (alpha - 2) \  \                 \

                                       1\                    3     
  [[-1], [1 - alpha]], [[-1, -1], []], -| GAMMA(-alpha) alpha  - 3 
                                       x/                          

   (-alpha)        /                                     1\             
  x         MeijerG|[[-1], [1 - alpha]], [[-1, -1], []], -| GAMMA(-alpha
                   \                                     x/             

         2      (-alpha)                            /
  ) alpha  + 2 x         GAMMA(-alpha) alpha MeijerG|
                                                    \

                                       1\    (2 - alpha)\\
  [[-1], [1 - alpha]], [[-1, -1], []], -| + x           ||
                                       x/               //

@Rouben Rostamian  

Thanks you are right.

How if we change r to abs(r)

 

 

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