adel-00

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11 years, 13 days

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These are replies submitted by adel-00

@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)

 

 

@Carl Love 

Thanks Carl for all your comments and your valuable efforts.

The expressions are very complicated to solve the integration symbolically.

So I tried the basic way to solve it approximately (by summation).

thamks agian @Carl Love  and @acer

 

 

@acer 

the code is doing integration whic is the summation by simpson rule

@acer 

Thanks ace

last polint in this line

sum1[n]:=2*(L[n]+sum1[n-1])/3;

 

how can i separte the summation of the even position and the odd as sum1[2n]=2*(L1[2n]+sum1[2n-1]) and for the odd be sum1[2n+1]=L1[2n+1]+sum1

 

@tomleslie 

thanks,

how can i calculate the last line which is the summation of L1[n] from -10 to 10

@Carl Love @tomleslie

Thanks for all ur reply

I guess this code need a litle improvement and will work

plsease check thisnew_code.mw

@Carl Love 

you are right about r. 

numerical_int.mw

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