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1 dependent and 2 independent variables....

SHIVAS 35 Maple 2018
syntax homework pde
September 06 2023
1 6

modifed_practice.mw

Impact of Shape-Dependent Hybrid Nanofluid on Transient Efficiency of a Fully W
et Porous Longitudinal Fin

dear sir please help me to solve the graph i given reference pdf also. i have implimented the code but getting error in ploting 

Thank you

DTM method with Dsolve method comparisio...

SHIVAS 35 Maple 2018
ode homework dsolve
August 18 2023
0 0

how to plot graphs for both methods and comparison of different method values for Diff(f(eta),eta, eta) at eta =0

 

> 

NULL
> 

NULL
> 

restart
> 

F[0] := al
> 

F[1] := a2
> 

F[2] := a3
> 

F[3] := a4
> 

G[0] := a5
> 

G[1] := a6
> 

T[0] := a7
> 

T[1] := a8
> 

Q[0] := a9
> 

Q[1] := a10
> 

n[1] := 1
> 

for k from 0 to n[1] do F[k+4] := solve((1+a)*(k+1)*(k+2)*(k+3)*(k+4)*F[k+4]-a*(k+1)*(k+2)*G[k+2]-R*(sum(F[k-m]*(m+1)*(m+2)*(m+3)*F[m+3], m = 0 .. k))+R*(sum((k-m+1)*F[k-m+1]*(m+1)*(m+2)*F[m+2], m = 0 .. k)), F[k+4]) end do

-(1/12)*(R*a2*a3-3*R*a4*al-a*G[2])/(1+a)

  

-(1/60)*(R^2*a2*a3*al-3*R^2*a4*al^2+2*R*a*a3^2-R*a*al*G[2]+2*R*a3^2-3*a^2*G[3]-3*a*G[3])/(1+a)^2

 (1)
> 

n[2] := 3
> 

for k from 0 to n[2] do G[k+2] := solve(b*(k+1)*(k+2)*G[k+2]+a*(k+1)*(k+2)*F[k+2]-2*a*G[k]-c*R*(sum((m+1)*G[m+1]*F[k-m], m = 0 .. k))+c*R*(sum(G[k-m]*(m+1)*F[m+1], m = 0 .. k)), G[k+2]) end do

-(1/2)*(R*a2*a5*c-R*a6*al*c+2*a*a3-2*a*a5)/b

  

-(1/6)*(R^2*a2*a5*al*c^2-R^2*a6*al^2*c^2+2*R*a*a3*al*c-2*R*a*a5*al*c+2*R*a3*a5*b*c+6*a*a4*b-2*a*a6*b)/b^2

  

-(1/24)*(R^3*a*a2*a5*al^2*c^3-R^3*a*a6*al^3*c^3+R^3*a2*a5*al^2*c^3-R^3*a6*al^3*c^3+2*R^2*a^2*a3*al^2*c^2-2*R^2*a^2*a5*al^2*c^2+R^2*a*a2^2*a5*b*c^2-R^2*a*a2*a6*al*b*c^2+2*R^2*a*a3*a5*al*b*c^2+2*R^2*a*a3*al^2*c^2-2*R^2*a*a5*al^2*c^2+R^2*a2^2*a5*b*c^2-R^2*a2*a6*al*b*c^2+2*R^2*a3*a5*al*b*c^2+2*R*a^2*a2*a3*b*c-R*a^2*a2*a5*b*c+6*R*a^2*a4*al*b*c-3*R*a^2*a6*al*b*c+2*R*a*a3*a6*b^2*c+6*R*a*a4*a5*b^2*c-2*R*a*a2*a3*b^2+2*R*a*a2*a3*b*c+6*R*a*a4*al*b^2+6*R*a*a4*al*b*c-4*R*a*a6*al*b*c+2*R*a3*a6*b^2*c+6*R*a4*a5*b^2*c+2*a^3*a3*b-2*a^3*a5*b+4*a^2*a3*b-4*a^2*a5*b)/(b^3*(1+a))

  

-(1/120)*(R^4*a^2*a2*a5*al^3*c^4-R^4*a^2*a6*al^4*c^4+2*R^4*a*a2*a5*al^3*c^4-2*R^4*a*a6*al^4*c^4+R^4*a2*a5*al^3*c^4-R^4*a6*al^4*c^4+2*R^3*a^3*a3*al^3*c^3-2*R^3*a^3*a5*al^3*c^3+3*R^3*a^2*a2^2*a5*al*b*c^3-3*R^3*a^2*a2*a6*al^2*b*c^3+2*R^3*a^2*a3*a5*al^2*b*c^3+4*R^3*a^2*a3*al^3*c^3-4*R^3*a^2*a5*al^3*c^3+6*R^3*a*a2^2*a5*al*b*c^3-6*R^3*a*a2*a6*al^2*b*c^3+4*R^3*a*a3*a5*al^2*b*c^3+2*R^3*a*a3*al^3*c^3-2*R^3*a*a5*al^3*c^3+3*R^3*a2^2*a5*al*b*c^3-3*R^3*a2*a6*al^2*b*c^3+2*R^3*a3*a5*al^2*b*c^3+6*R^2*a^3*a2*a3*al*b*c^2-4*R^2*a^3*a2*a5*al*b*c^2+6*R^2*a^3*a4*al^2*b*c^2-4*R^2*a^3*a6*al^2*b*c^2+4*R^2*a^2*a2*a3*a5*b^2*c^2-R^2*a^2*a2*a5^2*b^2*c^2+2*R^2*a^2*a3*a6*al*b^2*c^2+6*R^2*a^2*a4*a5*al*b^2*c^2+R^2*a^2*a5*a6*al*b^2*c^2-2*R^2*a^2*a2*a3*al*b^2*c+12*R^2*a^2*a2*a3*al*b*c^2-R^2*a^2*a2*a5*al*b^2*c-6*R^2*a^2*a2*a5*al*b*c^2+6*R^2*a^2*a4*al^2*b^2*c+12*R^2*a^2*a4*al^2*b*c^2+R^2*a^2*a6*al^2*b^2*c-10*R^2*a^2*a6*al^2*b*c^2-2*R^2*a*a2*a3*a5*b^3*c+8*R^2*a*a2*a3*a5*b^2*c^2-R^2*a*a2*a5^2*b^2*c^2+4*R^2*a*a3*a6*al*b^2*c^2+6*R^2*a*a4*a5*al*b^3*c+12*R^2*a*a4*a5*al*b^2*c^2+R^2*a*a5*a6*al*b^2*c^2-2*R^2*a*a2*a3*al*b^3-2*R^2*a*a2*a3*al*b^2*c+6*R^2*a*a2*a3*al*b*c^2-2*R^2*a*a2*a5*al*b*c^2+6*R^2*a*a4*al^2*b^3+6*R^2*a*a4*al^2*b^2*c+6*R^2*a*a4*al^2*b*c^2-6*R^2*a*a6*al^2*b*c^2-2*R^2*a2*a3*a5*b^3*c+4*R^2*a2*a3*a5*b^2*c^2+2*R^2*a3*a6*al*b^2*c^2+6*R^2*a4*a5*al*b^3*c+6*R^2*a4*a5*al*b^2*c^2+4*R*a^4*a3*al*b*c-4*R*a^4*a5*al*b*c+12*R*a^3*a2*a4*b^2*c-4*R*a^3*a2*a6*b^2*c+2*R*a^3*a5^2*b^2*c+12*R*a^2*a4*a6*b^3*c-2*R*a^3*a3*al*b^2+12*R*a^3*a3*al*b*c+2*R*a^3*a5*al*b^2-12*R*a^3*a5*al*b*c+24*R*a^2*a2*a4*b^2*c-8*R*a^2*a2*a6*b^2*c-4*R*a^2*a3^2*b^3+4*R*a^2*a3*a5*b^2*c+2*R*a^2*a5^2*b^2*c+24*R*a*a4*a6*b^3*c+8*R*a^2*a3*al*b*c-8*R*a^2*a5*al*b*c+12*R*a*a2*a4*b^2*c-4*R*a*a2*a6*b^2*c-4*R*a*a3^2*b^3+4*R*a*a3*a5*b^2*c+12*R*a4*a6*b^3*c+6*a^4*a4*b^2-2*a^4*a6*b^2+18*a^3*a4*b^2-6*a^3*a6*b^2+12*a^2*a4*b^2-4*a^2*a6*b^2)/(b^4*(1+a)^2)

 (2)
> 

n[3] := 3
> 

for k from 0 to n[3] do T[k+2] := solve((k+1)*(k+2)*T[k+2]+p3*(k+1)*(k+2)*Q[k+2]+p1*(sum((m+1)*F[m+1]*T[k-m], m = 0 .. k))-p1*(sum(F[k-m]*(m+1)*T[m+1], m = 0 .. k)), T[k+2]) end do

-(1/2)*p1*a2*a7+(1/2)*p1*al*a8-p3*Q[2]

  

-(1/6)*a2*a7*al*p1^2+(1/6)*a8*al^2*p1^2-(1/3)*al*p1*p3*Q[2]-(1/3)*a3*a7*p1-p3*Q[3]

  

-p3*Q[4]-(1/24)*p1^2*a2^2*a7+(1/24)*a2*p1^2*al*a8-(1/12)*p1*a2*p3*Q[2]-(1/12)*p1*a3*a8-(1/4)*p1*a4*a7-(1/24)*a2*a7*al^2*p1^3+(1/24)*a8*al^3*p1^3-(1/12)*al^2*p1^2*p3*Q[2]-(1/12)*al*a3*a7*p1^2-(1/4)*p1*al*p3*Q[3]

  

(1/120)*(-a*a2*a7*al^3*b*p1^4+a*a8*al^4*b*p1^4-2*a*al^3*b*p1^3*p3*Q[2]-a2*a7*al^3*b*p1^4+a8*al^4*b*p1^4-3*a*a2^2*a7*al*b*p1^3+3*a*a2*a8*al^2*b*p1^3-2*a*a3*a7*al^2*b*p1^3-2*al^3*b*p1^3*p3*Q[2]-6*a*a2*al*b*p1^2*p3*Q[2]-6*a*al^2*b*p1^2*p3*Q[3]-3*a2^2*a7*al*b*p1^3+3*a2*a8*al^2*b*p1^3-2*a3*a7*al^2*b*p1^3+R*a*a2*a5*a7*c*p1-R*a*a6*a7*al*c*p1-4*a*a2*a3*a7*b*p1^2-2*a*a3*a8*al*b*p1^2-6*a*a4*a7*al*b*p1^2-6*a2*al*b*p1^2*p3*Q[2]-6*al^2*b*p1^2*p3*Q[3]+2*R*a2*a3*a7*b*p1-6*R*a4*a7*al*b*p1-12*a*a2*b*p1*p3*Q[3]-24*a*al*b*p1*p3*Q[4]-4*a2*a3*a7*b*p1^2-2*a3*a8*al*b*p1^2-6*a4*a7*al*b*p1^2+2*a^2*a3*a7*p1-2*a^2*a5*a7*p1-12*a*a4*a8*b*p1-12*a2*b*p1*p3*Q[3]-24*al*b*p1*p3*Q[4]-120*a*b*p3*Q[5]-12*a4*a8*b*p1-120*b*p3*Q[5])/(b*(1+a))

 (3)
> 

n[4] := 3
> 

for k from 0 to n[4] do Q[k+2] := solve((k+1)*(k+2)*Q[k+2]+p4*(k+1)*(k+2)*Q[k+2]+p2*(sum((m+1)*F[m+1]*Q[k-m], m = 0 .. k))-p2*(sum(F[k-m]*(m+1)*Q[m+1], m = 0 .. k)), Q[k+2]) end do

(1/2)*p2*(a10*al-a2*a9)/(p4+1)

  

(1/6)*p2*(a10*al^2*p2-a2*a9*al*p2-2*a3*a9*p4-2*a3*a9)/(p4+1)^2

  

(1/24)*p2*(a10*al^3*p2^2-a2*a9*al^2*p2^2+a10*a2*al*p2*p4-a2^2*a9*p2*p4-2*a3*a9*al*p2*p4+a10*a2*al*p2-2*a10*a3*p4^2-a2^2*a9*p2-2*a3*a9*al*p2-6*a4*a9*p4^2-4*a10*a3*p4-12*a4*a9*p4-2*a10*a3-6*a4*a9)/(p4+1)^3

  

(1/120)*p2*(a*a10*al^4*b*p2^3-a*a2*a9*al^3*b*p2^3+R*a*a2*a5*a9*c*p4^3-R*a*a6*a9*al*c*p4^3+3*a*a10*a2*al^2*b*p2^2*p4-3*a*a2^2*a9*al*b*p2^2*p4-2*a*a3*a9*al^2*b*p2^2*p4+a10*al^4*b*p2^3-a2*a9*al^3*b*p2^3+3*R*a*a2*a5*a9*c*p4^2-3*R*a*a6*a9*al*c*p4^2+2*R*a2*a3*a9*b*p4^3-6*R*a4*a9*al*b*p4^3+3*a*a10*a2*al^2*b*p2^2-2*a*a10*a3*al*b*p2*p4^2-3*a*a2^2*a9*al*b*p2^2-4*a*a2*a3*a9*b*p2*p4^2-2*a*a3*a9*al^2*b*p2^2-6*a*a4*a9*al*b*p2*p4^2+3*a10*a2*al^2*b*p2^2*p4-3*a2^2*a9*al*b*p2^2*p4-2*a3*a9*al^2*b*p2^2*p4+3*R*a*a2*a5*a9*c*p4-3*R*a*a6*a9*al*c*p4+6*R*a2*a3*a9*b*p4^2-18*R*a4*a9*al*b*p4^2+2*a^2*a3*a9*p4^3-2*a^2*a5*a9*p4^3-4*a*a10*a3*al*b*p2*p4-12*a*a10*a4*b*p4^3-8*a*a2*a3*a9*b*p2*p4-12*a*a4*a9*al*b*p2*p4+3*a10*a2*al^2*b*p2^2-2*a10*a3*al*b*p2*p4^2-3*a2^2*a9*al*b*p2^2-4*a2*a3*a9*b*p2*p4^2-2*a3*a9*al^2*b*p2^2-6*a4*a9*al*b*p2*p4^2+R*a*a2*a5*a9*c-R*a*a6*a9*al*c+6*R*a2*a3*a9*b*p4-18*R*a4*a9*al*b*p4+6*a^2*a3*a9*p4^2-6*a^2*a5*a9*p4^2-2*a*a10*a3*al*b*p2-36*a*a10*a4*b*p4^2-4*a*a2*a3*a9*b*p2-6*a*a4*a9*al*b*p2-4*a10*a3*al*b*p2*p4-12*a10*a4*b*p4^3-8*a2*a3*a9*b*p2*p4-12*a4*a9*al*b*p2*p4+2*R*a2*a3*a9*b-6*R*a4*a9*al*b+6*a^2*a3*a9*p4-6*a^2*a5*a9*p4-36*a*a10*a4*b*p4-2*a10*a3*al*b*p2-36*a10*a4*b*p4^2-4*a2*a3*a9*b*p2-6*a4*a9*al*b*p2+2*a^2*a3*a9-2*a^2*a5*a9-12*a*a10*a4*b-36*a10*a4*b*p4-12*a10*a4*b)/((p4+1)^4*b*(1+a))

 (4)
> 

U[1] := sum(F[r]*t^r, r = 0 .. n[1]+4)
> 

p[1] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[1])
> 

U[2] := sum(G[r]*t^r, r = 0 .. n[2]+2)
> 

p[2] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[2])
> 

U[3] := sum(T[r]*t^r, r = 0 .. n[2]+2)
> 

p[3] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[3])
> 

U[4] := sum(Q[r]*t^r, r = 0 .. n[2]+2)
> 

p[4] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[4])
> 

e1 := subs(t = -1, p[1]) = 0
> 

e2 := subs(t = -1, diff(p[1], t)) = 0
> 

e3 := subs(t = 1, diff(p[1], t)) = -1
> 

e4 := subs(t = 1, p[1]) = 0
> 

e5 := subs(t = -1, p[2]) = 0
> 

e6 := subs(t = 1, p[2]) = 1
> 

e7 := subs(t = -1, p[3]) = 1
> 

e8 := subs(t = 1, p[3]) = 0
> 

e9 := subs(t = -1, p[4]) = 1
> 

e10 := subs(t = 1, p[4]) = 0
> 

j := {e1, e10, e2, e3, e4, e5, e6, e7, e8, e9}
> 

j := solve(j)
> 

sj := evalf(j)

{a10 = -3.476623407, a2 = -5.754056209, a3 = .1776219452, a4 = 11.75811242, a5 = 1.324264301, a6 = -684.5523526, a7 = -.2700369914, a8 = 1.152227714, a9 = 2.191204245, al = 0.3618902741e-1}, {a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916}, {a10 = -4.849411034, a2 = 11.61910224, a3 = -20.01600142, a4 = -22.98820448, a5 = -303.7401922, a6 = -153.4446663, a7 = -7.896832028, a8 = -4.917031955, a9 = -9.645684059, al = 10.13300071}, {a10 = -12.41434918+6.055636678*I, a2 = -6.912869603-3.362489448*I, a3 = -9.364948739-.7062944755*I, a4 = 14.07573921+6.724978896*I, a5 = -106.6284397-3.087774395*I, a6 = 184.4202683+38.56644530*I, a7 = 2.689687372-4.048821750*I, a8 = -4.715343127+5.167588829*I, a9 = 8.474095612-5.785653488*I, al = 4.807474369+.3531472377*I}, {a10 = -8.462156658-37.78952093*I, a2 = -22.10322629+.7748996783*I, a3 = -2.926063539-87.71943544*I, a4 = 44.45645258-1.549799357*I, a5 = 126.1645842+1357.517358*I, a6 = -880.5344239+73.01362458*I, a7 = -96.56841781+19.40514883*I, a8 = -11.30265439-58.49348719*I, a9 = -59.25678527+13.86225901*I, al = 1.588031769+43.85971772*I}, {a10 = 21.28781597+0.9115942334e-2*I, a2 = -2.190767380-.1297694199*I, a3 = 0.4834062985e-1-8.617807139*I, a4 = 4.631534761+.2595388398*I, a5 = -1.070222696-4.103740084*I, a6 = 28.93315819+1.060309794*I, a7 = -.6440073083+2.959900705*I, a8 = 3.178056838-1.712994921*I, a9 = -1.124006374+8.865509135*I, al = .1008296851+4.308903570*I}, {a10 = -2.226772562-4.893664011*I, a2 = -5.213384606-.4953312060*I, a3 = 1.881656676-24.64377975*I, a4 = 10.67676921+.9906624121*I, a5 = -5.922885277-14.38776520*I, a6 = 9.281006594-6.268746147*I, a7 = -8.563253672+2.519226454*I, a8 = -2.293245547-7.112743663*I, a9 = -4.948019289+2.035858706*I, al = -.8158283379+12.32188987*I}, {a10 = -3.311080211+1.380948844*I, a2 = -6.825505968+3.517539795*I, a3 = 10.11566715-.6387142267*I, a4 = 13.90101194-7.035079589*I, a5 = 106.6696011-4.144959139*I, a6 = 183.4179274-43.03852019*I, a7 = -1.117431335-0.4722817327e-1*I, a8 = -1.705921790+.2164542338*I, a9 = -2.431505210+.6185873236*I, al = -4.932833576+.3193571133*I}, {a10 = 1.720689325, a2 = 11.30494181, a3 = 20.89441402, a4 = -22.35988362, a5 = 304.5741226, a6 = -141.0519632, a7 = -3.607319024, a8 = 2.107261122, a9 = -3.764007990, al = -10.32220701}, {a10 = -3.311080211-1.380948844*I, a2 = -6.825505968-3.517539795*I, a3 = 10.11566715+.6387142267*I, a4 = 13.90101194+7.035079589*I, a5 = 106.6696011+4.144959139*I, a6 = 183.4179274+43.03852019*I, a7 = -1.117431335+0.4722817327e-1*I, a8 = -1.705921790-.2164542338*I, a9 = -2.431505210-.6185873236*I, al = -4.932833576-.3193571133*I}, {a10 = -2.226772562+4.893664011*I, a2 = -5.213384606+.4953312060*I, a3 = 1.881656676+24.64377975*I, a4 = 10.67676921-.9906624121*I, a5 = -5.922885277+14.38776520*I, a6 = 9.281006594+6.268746147*I, a7 = -8.563253672-2.519226454*I, a8 = -2.293245547+7.112743663*I, a9 = -4.948019289-2.035858706*I, al = -.8158283379-12.32188987*I}, {a10 = 21.28781597-0.9115942334e-2*I, a2 = -2.190767380+.1297694199*I, a3 = 0.4834062985e-1+8.617807139*I, a4 = 4.631534761-.2595388398*I, a5 = -1.070222696+4.103740084*I, a6 = 28.93315819-1.060309794*I, a7 = -.6440073083-2.959900705*I, a8 = 3.178056838+1.712994921*I, a9 = -1.124006374-8.865509135*I, al = .1008296851-4.308903570*I}, {a10 = -8.462156658+37.78952093*I, a2 = -22.10322629-.7748996783*I, a3 = -2.926063539+87.71943544*I, a4 = 44.45645258+1.549799357*I, a5 = 126.1645842-1357.517358*I, a6 = -880.5344239-73.01362458*I, a7 = -96.56841781-19.40514883*I, a8 = -11.30265439+58.49348719*I, a9 = -59.25678527-13.86225901*I, al = 1.588031769-43.85971772*I}, {a10 = -12.41434918-6.055636678*I, a2 = -6.912869603+3.362489448*I, a3 = -9.364948739+.7062944755*I, a4 = 14.07573921-6.724978896*I, a5 = -106.6284397+3.087774395*I, a6 = 184.4202683-38.56644530*I, a7 = 2.689687372+4.048821750*I, a8 = -4.715343127-5.167588829*I, a9 = 8.474095612+5.785653488*I, al = 4.807474369-.3531472377*I}

 (5)
> 

p[1] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[1])

.2586309916+.2575353882*t-.2672619833*t^2-.2650707765*t^3+0.8630991633e-2*t^4+0.7535388242e-2*t^5

 (6)
> 

p[2] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[2])

0.7065354871e-1+.1172581545*t+.3439809338*t^2+.3401058738*t^3+0.8536551748e-1*t^4+0.4263597162e-1*t^5

 (7)
> 

p[3] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[3])

.6100817436-.5277387253*t-.1364241818*t^2+0.3945483872e-1*t^3+0.2634243820e-1*t^4-0.1171611337e-1*t^5

 (8)
> 

p[4] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[4])

.5842364534-.5218741555*t-.1037943244*t^2+0.3134539737e-1*t^3+0.1955787096e-1*t^4-0.9471241840e-2*t^5

 (9)
> 

NULL
> 

value*of*D@@2*F(0)*For*R = 1, 1.5, `and`(2*Using*Both*DTM*scheme, dsolve*method)
> 

 

Download DTM_practice.mw

error in Pde plot ...

SHIVAS 35 Maple 2018
homework pde numeric
July 29 2023
1 6
> 

restart; with(plots)
> 

``
> 

Sc := 1; sigma := 5; E := 1; delta := 1; n := .5; Pr := .71; alphac := .1; alphat := .1; Lt := .1; Br := .1; Rd := 2; deltaB := .1
``
> 

OdeSys := {(diff(Theta(xi, eta), eta, eta))/Pr+(1/2)*(1-xi)*eta*(diff(Theta(xi, eta), eta))+xi*f(xi, eta)*(diff(Theta(xi, eta), eta))-xi*(1-xi)*(diff(Theta(xi, eta), xi)), diff(h(xi, eta), eta, eta)+(1/2)*(1-xi)*eta*(diff(f(xi, eta), eta))+xi*(f(xi, eta)*(diff(h(xi, eta), eta))-(diff(f(xi, eta), eta))*h(xi, eta)-2*lambda*(diff(f(xi, eta), eta)))-xi*(1-xi)*(diff(h(xi, eta), xi)), diff(f(xi, eta), eta, eta, eta)+(1/2)*(1-xi)*eta*(diff(f(xi, eta), eta, eta))+xi*(f(xi, eta)*(diff(f(xi, eta), eta, eta))-(diff(f(xi, eta), eta))*(diff(f(xi, eta), eta))+2*lambda*h(xi, eta))-xi*(1-xi)*(diff(diff(f(xi, eta), eta), xi)), (diff(Phi(xi, eta), eta, eta))/Sc+(1/2)*(1-xi)*eta*(diff(Phi(xi, eta), eta))+xi*f(xi, eta)*(diff(Phi(xi, eta), eta))-(sigma*sigma)*xi*Phi(xi, eta)*(1+n*delta*Theta(xi, eta))*exp(-E/(1+delta*Theta(xi, eta)))-xi*(1-xi)*(diff(Phi(xi, eta), xi))}; Cond := {Phi(0, eta) = 0, Phi(xi, 0) = 1, Phi(xi, 10) = 0, Theta(0, eta) = 0, Theta(xi, 0) = 1, Theta(xi, 10) = 0, f(0, eta) = 0, f(xi, 0) = 0, h(0, eta) = 0, h(xi, 0) = 0, h(xi, 10) = 0, (D[2](f))(xi, 0) = 1, (D[2](f))(xi, 10) = 0}
> 

colour := [red, green, blue, gold]
> 

lambdaVals := [1, 1.5, 2, 3]
> 

for j to numelems(lambdaVals) do Ans[j] := pdsolve((eval([OdeSys, Cond], lambda = lambdaVals[j]))[], numeric); Ng[j] := eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j]))+Br*(xi*(eval(diff(f(xi, eta), eta), Ans[j]))-sin(xi))^2+(Br*xi*xi)*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^2-(1/3)*Br*deltaB*xi^4*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^4, lambda = lambdaVals[j]); Bj[j] := (eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j])), lambda = lambdaVals[j]))/(eval(alphat*(1+4*Rd*(1/3))*(eval(diff(Theta(xi, eta), eta), Ans[j]))^2+Lt*alphac*(eval(diff(Phi(xi, eta), eta), Ans[j]))^2/alphat+Lt*(eval(diff(Phi(xi, eta), eta), Ans[j]))*(eval(diff(Theta(xi, eta), eta), Ans[j]))+Br*(xi*(eval(diff(f(xi, eta), eta), Ans[j]))-sin(xi))^2+(Br*xi*xi)*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^2-(1/3)*Br*deltaB*xi^4*(eval(diff(f(xi, eta), eta, eta), Ans[j]))^4, lambda = lambdaVals[j])) end do

Error, invalid input: eval received _m2939359678144, which is not valid for its 2nd argument, eqns

  
> 

 

> 

plotA := plots:-display(seq(Ans[k]:-plot(Theta(xi, eta), xi = 1, eta = 0 .. 10, color = colour[k]), k = 1 .. nops(lambdaVals)), linestyle = "solid", thickness = 2)

Error, `Ans[k]` does not evaluate to a module

  
> 

plotB := plots:-display(seq(Ans[k]:-plot(Ng[j], xi = 1, eta = 0 .. 10, color = colour[k]), k = 1 .. nops(lambdaVals)), linestyle = "solid", thickness = 2)

Error, (in pdsolve/process_depspec) specified dependent functions cannot be evaluated in terms of the PDE solution, got extra indeterminates {Ng[1]}

  
> 

plotC := plots:-display(seq(Ans[k]:-plot(Bj[j], xi = 1, eta = 0 .. 10, color = colour[k]), k = 1 .. nops(lambdaVals)), linestyle = "solid", thickness = 2 );

Error, (in pdsolve/process_depspec) specified dependent functions cannot be evaluated in terms of the PDE solution, got extra indeterminates {Bj[1]}

  
> 

``

Download error_in_plot.mw

Help me to rectify the error 

What is the mistake?

in this worksheet

Crank–Nicolson Finite difference scheme ...

SHIVAS 35 Maple 2022
ode homework numeric
July 11 2023
0 3

How to get same graph from maple with finite difference method for differential equations 

I m new here how to plot this i have seen related posts no where given clear idea for FDM method

plase help me to get the results Thank you

 

 

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