## 135 Reputation

12 years, 306 days

## @  no complex number at all...

no complex number at all

## @Ali Guzel   it is run for 20 min ...

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

## @acer  thanks  do u mean&nbs...

thanks

do u mean explicit(solve(K1=0,R));

still no roots

## @Rouben Rostamian   The resean is ...

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...

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

## @tomleslie Thank you for your help....

I made changes in the Ics

 > 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]);
 >
 (1)
 >

## pde_2022.mwI dont know what is the error...

pde_2022.mw

I dont know what is the error

Many thanks

Many thanks

## @Carl Love  here the approximation...

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 ...

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...

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 comme...

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

## restart:assume(t,real):a:=1:alpha:=1.2:h...

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);

## I got this...

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/               //

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