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kencom1

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9 years, 75 days
UNIVERSITY OF LAGOS, AKOKA YABA, LAGOS
LAGOS, Nigeria

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Help with the loop...

kencom1 115 Maple
loop while
August 01 2018
1 0

Good day everyone,

          I am trying to write a code for the loop of the equations below such the Theta[k] and Phi[k] start from 2 to M while F[k] starts from 4  to M.

         Anyone with good informations should please.
         Below is the link.

Thanks in anticipation

Solution_1.mw

Finite difference Method...

kencom1 115 Maple
ode differential-equation numeric
July 18 2018
2 2

Good day everyone,

I am trying to write a finite difference Method solution for an ODE and its giving me problem solving the algebraic simplifications generated. Please, any one with useful informations. Below is the attached file

FDM1.mw
 

> 

restart
> 

with(ODETools)
> 

with(student)
> 

with(plots)
> 

with(plottools)
> 

xmin := 0; xmax := 6
> 

n := 60
> 

`σ__1` := .5
> 

ode:=diff(f(eta),eta$3)+f(eta)*diff(f(eta),eta$2)=0

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta)) = 0

 (1)
> 

bc1:=df(xmin)=2*sigma__1;

df(0) = 1.0

 (2)
> 

bc2:=d2f(xmin)=0;

d2f(0) = 0

 (3)
> 

bc3:=d3f(xmax)=2;

d3f(6) = 2

 (4)
> 

dfde:=proc(h)(f[k+1]-f[k-1])/2/h;end proc:
> 

dfde(h);

(1/2)*(f[k+1]-f[k-1])/h

 (5)
> 

d2fde2:=proc(h)(f[k+1]-2*f[k]+f[k-1])/h^2;end proc:
> 

d2fde2(h);

(f[k+1]-2*f[k]+f[k-1])/h^2

 (6)
> 

d3fde3:=proc(h)(f[k+1]-3*f[k]+3*f[k-1]-f[k-2])/h^3;end proc:
> 

d3fde3(h);

(f[k+1]-3*f[k]+3*f[k-1]-f[k-2])/h^3

 (7)
> 

d2fde2f:=proc(h)(f[k+2]-2*f[k+1]+f[k])/h^2;end proc:
> 

d2fde2f(h);

(f[k+2]-2*f[k+1]+f[k])/h^2

 (8)
> 

d2fde2b:=proc(h)(f[k]-2*f[k-1]+f[k-2])/h^2;end proc:
> 

d2fde2b(h);

(f[k]-2*f[k-1]+f[k-2])/h^2

 (9)
> 

 

> 

dfdef:=proc(h)(f[k+1]-f[k])/h;end proc:
> 

dfdef(h);

(f[k+1]-f[k])/h

 (10)
> 

h:=xmax/(n-1)

6/59

 (11)
> 

stencil:=subs(diff(f(eta),eta$3)=d3fde3(h),f(eta)=f[k],diff(f(eta),eta$2)=d2fde2,ode);

(205379/216)*f[k+1]-(205379/72)*f[k]+(205379/72)*f[k-1]-(205379/216)*f[k-2]+f[k]*(diff(diff(f[k], eta), eta)) = 0

 (12)
> 

bcEqs:=[subs(k=0,dfdef(h))=rhs(bc1),subs(k=0,d2fde2f(h))=rhs(bc2),
subs(k=n-1,d2fde2b(h))=rhs(bc3)];

[(59/6)*f[1]-(59/6)*f[0] = 1.0, (3481/36)*f[2]-(3481/18)*f[1]+(3481/36)*f[0] = 0, (3481/36)*f[59]-(3481/18)*f[58]+(3481/36)*f[57] = 2]

 (13)
> 

eqs:=Vector(n-2):
cnt:=0:

for k from 1 to n-2 do
    cnt:=cnt+1:
    eqs(cnt):=stencil;
end do:

eqs:
> 

eqs := [op(convert(eqs, list)), op(bcEqs)]; vars := [seq(f[k], k = 0 .. n-1)]; map(print, eqs)

(205379/216)*f[2]-(205379/72)*f[1]+(205379/72)*f[0]-(205379/216)*f[-1] = 0

  

(205379/216)*f[3]-(205379/72)*f[2]+(205379/72)*f[1]-(205379/216)*f[0] = 0

  

(205379/216)*f[4]-(205379/72)*f[3]+(205379/72)*f[2]-(205379/216)*f[1] = 0

  

(205379/216)*f[5]-(205379/72)*f[4]+(205379/72)*f[3]-(205379/216)*f[2] = 0

  

(205379/216)*f[6]-(205379/72)*f[5]+(205379/72)*f[4]-(205379/216)*f[3] = 0

  

(205379/216)*f[7]-(205379/72)*f[6]+(205379/72)*f[5]-(205379/216)*f[4] = 0

  

(205379/216)*f[8]-(205379/72)*f[7]+(205379/72)*f[6]-(205379/216)*f[5] = 0

  

(205379/216)*f[9]-(205379/72)*f[8]+(205379/72)*f[7]-(205379/216)*f[6] = 0

  

(205379/216)*f[10]-(205379/72)*f[9]+(205379/72)*f[8]-(205379/216)*f[7] = 0

  

(205379/216)*f[11]-(205379/72)*f[10]+(205379/72)*f[9]-(205379/216)*f[8] = 0

  

(205379/216)*f[12]-(205379/72)*f[11]+(205379/72)*f[10]-(205379/216)*f[9] = 0

  

(205379/216)*f[13]-(205379/72)*f[12]+(205379/72)*f[11]-(205379/216)*f[10] = 0

  

(205379/216)*f[14]-(205379/72)*f[13]+(205379/72)*f[12]-(205379/216)*f[11] = 0

  

(205379/216)*f[15]-(205379/72)*f[14]+(205379/72)*f[13]-(205379/216)*f[12] = 0

  

(205379/216)*f[16]-(205379/72)*f[15]+(205379/72)*f[14]-(205379/216)*f[13] = 0

  

(205379/216)*f[17]-(205379/72)*f[16]+(205379/72)*f[15]-(205379/216)*f[14] = 0

  

(205379/216)*f[18]-(205379/72)*f[17]+(205379/72)*f[16]-(205379/216)*f[15] = 0

  

(205379/216)*f[19]-(205379/72)*f[18]+(205379/72)*f[17]-(205379/216)*f[16] = 0

  

(205379/216)*f[20]-(205379/72)*f[19]+(205379/72)*f[18]-(205379/216)*f[17] = 0

  

(205379/216)*f[21]-(205379/72)*f[20]+(205379/72)*f[19]-(205379/216)*f[18] = 0

  

(205379/216)*f[22]-(205379/72)*f[21]+(205379/72)*f[20]-(205379/216)*f[19] = 0

  

(205379/216)*f[23]-(205379/72)*f[22]+(205379/72)*f[21]-(205379/216)*f[20] = 0

  

(205379/216)*f[24]-(205379/72)*f[23]+(205379/72)*f[22]-(205379/216)*f[21] = 0

  

(205379/216)*f[25]-(205379/72)*f[24]+(205379/72)*f[23]-(205379/216)*f[22] = 0

  

(205379/216)*f[26]-(205379/72)*f[25]+(205379/72)*f[24]-(205379/216)*f[23] = 0

  

(205379/216)*f[27]-(205379/72)*f[26]+(205379/72)*f[25]-(205379/216)*f[24] = 0

  

(205379/216)*f[28]-(205379/72)*f[27]+(205379/72)*f[26]-(205379/216)*f[25] = 0

  

(205379/216)*f[29]-(205379/72)*f[28]+(205379/72)*f[27]-(205379/216)*f[26] = 0

  

(205379/216)*f[30]-(205379/72)*f[29]+(205379/72)*f[28]-(205379/216)*f[27] = 0

  

(205379/216)*f[31]-(205379/72)*f[30]+(205379/72)*f[29]-(205379/216)*f[28] = 0

  

(205379/216)*f[32]-(205379/72)*f[31]+(205379/72)*f[30]-(205379/216)*f[29] = 0

  

(205379/216)*f[33]-(205379/72)*f[32]+(205379/72)*f[31]-(205379/216)*f[30] = 0

  

(205379/216)*f[34]-(205379/72)*f[33]+(205379/72)*f[32]-(205379/216)*f[31] = 0

  

(205379/216)*f[35]-(205379/72)*f[34]+(205379/72)*f[33]-(205379/216)*f[32] = 0

  

(205379/216)*f[36]-(205379/72)*f[35]+(205379/72)*f[34]-(205379/216)*f[33] = 0

  

(205379/216)*f[37]-(205379/72)*f[36]+(205379/72)*f[35]-(205379/216)*f[34] = 0

  

(205379/216)*f[38]-(205379/72)*f[37]+(205379/72)*f[36]-(205379/216)*f[35] = 0

  

(205379/216)*f[39]-(205379/72)*f[38]+(205379/72)*f[37]-(205379/216)*f[36] = 0

  

(205379/216)*f[40]-(205379/72)*f[39]+(205379/72)*f[38]-(205379/216)*f[37] = 0

  

(205379/216)*f[41]-(205379/72)*f[40]+(205379/72)*f[39]-(205379/216)*f[38] = 0

  

(205379/216)*f[42]-(205379/72)*f[41]+(205379/72)*f[40]-(205379/216)*f[39] = 0

  

(205379/216)*f[43]-(205379/72)*f[42]+(205379/72)*f[41]-(205379/216)*f[40] = 0

  

(205379/216)*f[44]-(205379/72)*f[43]+(205379/72)*f[42]-(205379/216)*f[41] = 0

  

(205379/216)*f[45]-(205379/72)*f[44]+(205379/72)*f[43]-(205379/216)*f[42] = 0

  

(205379/216)*f[46]-(205379/72)*f[45]+(205379/72)*f[44]-(205379/216)*f[43] = 0

  

(205379/216)*f[47]-(205379/72)*f[46]+(205379/72)*f[45]-(205379/216)*f[44] = 0

  

(205379/216)*f[48]-(205379/72)*f[47]+(205379/72)*f[46]-(205379/216)*f[45] = 0

  

(205379/216)*f[49]-(205379/72)*f[48]+(205379/72)*f[47]-(205379/216)*f[46] = 0

  

(205379/216)*f[50]-(205379/72)*f[49]+(205379/72)*f[48]-(205379/216)*f[47] = 0

  

(205379/216)*f[51]-(205379/72)*f[50]+(205379/72)*f[49]-(205379/216)*f[48] = 0

  

(205379/216)*f[52]-(205379/72)*f[51]+(205379/72)*f[50]-(205379/216)*f[49] = 0

  

(205379/216)*f[53]-(205379/72)*f[52]+(205379/72)*f[51]-(205379/216)*f[50] = 0

  

(205379/216)*f[54]-(205379/72)*f[53]+(205379/72)*f[52]-(205379/216)*f[51] = 0

  

(205379/216)*f[55]-(205379/72)*f[54]+(205379/72)*f[53]-(205379/216)*f[52] = 0

  

(205379/216)*f[56]-(205379/72)*f[55]+(205379/72)*f[54]-(205379/216)*f[53] = 0

  

(205379/216)*f[57]-(205379/72)*f[56]+(205379/72)*f[55]-(205379/216)*f[54] = 0

  

(205379/216)*f[58]-(205379/72)*f[57]+(205379/72)*f[56]-(205379/216)*f[55] = 0

  

(205379/216)*f[59]-(205379/72)*f[58]+(205379/72)*f[57]-(205379/216)*f[56] = 0

  

(59/6)*f[1]-(59/6)*f[0] = 1.0

  

(3481/36)*f[2]-(3481/18)*f[1]+(3481/36)*f[0] = 0

  

(3481/36)*f[59]-(3481/18)*f[58]+(3481/36)*f[57] = 2

 (14)
> 

sol := fsolve([op(eqs)])

{f[-1] = 74076407.16, f[0] = 74076407.19, f[1] = 74076407.29, f[2] = 74076407.42, f[3] = 74076407.63, f[4] = 74076407.95, f[5] = 74076408.39, f[6] = 74076408.95, f[7] = 74076409.58, f[8] = 74076410.32, f[9] = 74076411.18, f[10] = 74076412.19, f[11] = 74076413.34, f[12] = 74076414.66, f[13] = 74076416.09, f[14] = 74076417.69, f[15] = 74076419.41, f[16] = 74076421.28, f[17] = 74076423.28, f[18] = 74076425.45, f[19] = 74076427.75, f[20] = 74076430.17, f[21] = 74076432.77, f[22] = 74076435.56, f[23] = 74076438.51, f[24] = 74076441.69, f[25] = 74076445.02, f[26] = 74076448.54, f[27] = 74076452.24, f[28] = 74076456.15, f[29] = 74076460.29, f[30] = 74076464.65, f[31] = 74076469.16, f[32] = 74076473.82, f[33] = 74076478.70, f[34] = 74076483.79, f[35] = 74076489.05, f[36] = 74076494.52, f[37] = 74076500.21, f[38] = 74076506.15, f[39] = 74076512.33, f[40] = 74076518.79, f[41] = 74076525.57, f[42] = 74076532.68, f[43] = 74076540.10, f[44] = 74076547.80, f[45] = 74076555.85, f[46] = 74076564.23, f[47] = 74076572.94, f[48] = 74076581.93, f[49] = 74076591.18, f[50] = 74076600.60, f[51] = 74076610.20, f[52] = 74076620.03, f[53] = 74076630.05, f[54] = 74076640.28, f[55] = 74076650.64, f[56] = 74076661.19, f[57] = 74076671.90, f[58] = 74076682.68, f[59] = 74076693.50}

 (15)
> 

``


 

Download FDM1.mw

 

invalid subscript selector...

kencom1 115 Maple
indexing dsolve
June 25 2018
2 2

Goodday everyone,

Please, anyone with useful informations on the above stated error code should help.

Below is the attached file.

Error_invalid_subscript_selector.mw

Thanks in anticipation for your response

Error, unable to compute coeff...

kencom1 115 Maple
coeff coefficients
June 12 2018
2 0

Hello everyone, 

         Anyone with the solutions to the error code "Error, unable to compute coeff" should please help. 

         Attached below is the code.

         Thanking you in anticipations for your prompt response. 

Hpm_1.mw

Error, final value in for loop must be n...

kencom1 115 Maple
syntax loop
May 07 2018
1 0

Goodday sirs, 

            How can I get over these error message123.mw
 

> 

restart
> 

 
 

(int((1/6)*(eta-s)^3*(S*(s*f[i](s)+3*(diff(diff(f[i](s), s), s))+(diff(f[i](s), s))*(diff(diff(f[i](s), s), s))-f[i]*(diff(diff(diff(f[i](s), s), s), s)))+M^2*(diff(diff(f[i](s), s), s))), s = 0 .. eta))/(1+1/y)

 (1)
> 

G := (int((eta-s)^3*(S*(s*f[i](s)+3*(diff(f[i](s), `$`(s, 2)))+(diff(f[i](s), s))*(diff(f[i](s), `$`(s, 2)))-f[i]*(diff(f[i](s), `$`(s, 3))))+M^2*(diff(f[i](s), `$`(s, 2))))/factorial(3), s = 0 .. eta))/(1+1/y)
 
> 

f[0] := (1/6)*s+(1/6)*s^3:
> 

for i from 0 to n do f[i+1] := (1/6*(-eta^3+eta))*subs(eta = 1, diff(G, `$`(eta, 2)))-eta*subs(eta = G)+G; f[i+1] := subs(eta = s, f[i+1]) end do

Error, final value in for loop must be numeric or character

  
> 

``


Anyone with useful informations please.

Thanking you in anticipation for a favurabke response

Download 123.mw

 

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