kencom1

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6 years, 245 days
UNIVERSITY OF LAGOS, AKOKA YABA, LAGOS
LAGOS, Nigeria

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These are questions asked by kencom1

Good day everyone,

I have a problem building the code attached below. The series is not substituting F[0](eta) and T[0](eta). 

Please, anyone with useful information should contact.

Thanks

HAM_build.mw

Good day everyone,

I am trying to write HAM code for coupled ODE but getting errors like "table(...)" or

 

"Error, (in dsolve) found the independent variables {eta} also present in the names of the functions of the system {(diff(diff(diff((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; eta*exp(-eta)-F[w] end proc ] ))(eta), eta), eta), eta))(f[1](eta)), (diff(diff((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; exp(-eta) end proc ] ))(eta), eta), eta))(theta[1](eta)), (diff((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; eta*exp(-eta)-F[w] end proc ] ))(eta), eta))(f[1](eta)), ((table( [( 0 ) = proc (eta) options operator, arrow, function_assign; exp(-eta) end proc ] ))(eta))(theta[1](eta))}"

 

Anyone with useful informations should please help.

Thank you.

Below is the attached of the file

untitled22222.m

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

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

 

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

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