Advanced Search

faisal

15 Reputation

4 Badges

7 years, 171 days
Contact faisal

MaplePrimes Activity


These are questions asked by faisal

how to compUTE CPU time in RK45 dsolve ...

faisal 15 Maple
dsolve numeric timing
June 22 2016
2 0

 

DEAR SIR

ANYONE CAN HELP TO COMPUTE TIME IN DSOLVE COMMAND?

> 

restart
> 

with(plots)
> 

Nb := 0.1e-4; Nt := 0.1e-4; Sc := 3.0; Sb := 15; Pe := 1; Bi := .5; Pr := 6.8; c[4] := 0; c[6] := .3; c[8] := .4; k[1] := 0; k[2] := 1; k[3] := 0; Un := .1; M := .5
> 

Eq1 := (101-100*lambda)*(1+c[2]*phi(eta))*(diff(f(eta), `$`(eta, 3)))+(diff(f(eta), `$`(eta, 2)))*(f(eta)+g(eta)+c[2]*(diff(phi(eta), eta)))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta)-k[2])+k[2]+Un*(k[2]-(1/2)*eta*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))) = 0

(101-100*lambda)*(1+c[2]*phi(eta))*(diff(diff(diff(f(eta), eta), eta), eta))+(diff(diff(f(eta), eta), eta))*(f(eta)+g(eta)+c[2]*(diff(phi(eta), eta)))-(diff(f(eta), eta))^2-.6*(diff(f(eta), eta))+1.6-0.5000000000e-1*eta*(diff(diff(f(eta), eta), eta)) = 0

 (1)
> 

Eq2 := (101-100*lambda)*(1+c[2]*phi(eta))*(diff(g(eta), `$`(eta, 3)))+(diff(g(eta), `$`(eta, 2)))*(f(eta)+g(eta)+c[2]*(diff(phi(eta), eta)))-(diff(g(eta), eta))^2-M*(diff(g(eta), eta)-k[2])+k[2]+Un*(k[2]-(1/2)*eta*(diff(g(eta), `$`(eta, 2)))-(diff(g(eta), eta))) = 0

(101-100*lambda)*(1+c[2]*phi(eta))*(diff(diff(diff(g(eta), eta), eta), eta))+(diff(diff(g(eta), eta), eta))*(f(eta)+g(eta)+c[2]*(diff(phi(eta), eta)))-(diff(g(eta), eta))^2-.6*(diff(g(eta), eta))+1.6-0.5000000000e-1*eta*(diff(diff(g(eta), eta), eta)) = 0

 (2)
> 

Eq3 := (1+c[4]*phi(eta))*(diff(theta(eta), `$`(eta, 2)))+Pr*(diff(theta(eta), eta))*(f(eta)+g(eta))+Nb*Pr*(diff(theta(eta), eta))*(diff(phi(eta), eta))*(1+c[6]*(2*phi(eta)+1))+Nt*Pr*(diff(theta(eta), eta))^2+c[4]*(diff(theta(eta), eta))*(diff(phi(eta), eta))-(1/2)*Pr*eta*Un*(diff(theta(eta), eta)) = 0

diff(diff(theta(eta), eta), eta)+6.8*(diff(theta(eta), eta))*(f(eta)+g(eta))+0.68e-4*(diff(theta(eta), eta))*(diff(phi(eta), eta))*(1.3+.6*phi(eta))+0.68e-4*(diff(theta(eta), eta))^2-.3400000000*eta*(diff(theta(eta), eta)) = 0

 (3)
> 

Eq4 := (1+c[6]*phi(eta))*(diff(phi(eta), `$`(eta, 2)))+Sc*(f(eta)+g(eta))*(diff(phi(eta), eta))+c[6]*(diff(phi(eta), eta))^2+Nt*(diff(theta(eta), `$`(eta, 2)))/Nb-(1/2)*Sc*eta*Un*(diff(phi(eta), eta)) = 0

(1+.3*phi(eta))*(diff(diff(phi(eta), eta), eta))+3.0*(f(eta)+g(eta))*(diff(phi(eta), eta))+.3*(diff(phi(eta), eta))^2+1.000000000*(diff(diff(theta(eta), eta), eta))-.1500000000*eta*(diff(phi(eta), eta)) = 0

 (4)
> 

Eq5 := (1+c[8]*phi(eta))*(diff(chi(eta), `$`(eta, 2)))+c[8]*(diff(phi(eta), eta))*(diff(chi(eta), eta))-Pe*(chi(eta)*(diff(phi(eta), `$`(eta, 2)))+(diff(phi(eta), eta))*(diff(chi(eta), eta)))+Sb*(diff(chi(eta), eta))*(f(eta)+g(eta))-(1/2)*Sb*eta*Un*(diff(chi(eta), eta)) = 0

(1+.4*phi(eta))*(diff(diff(chi(eta), eta), eta))-.6*(diff(phi(eta), eta))*(diff(chi(eta), eta))-chi(eta)*(diff(diff(phi(eta), eta), eta))+15*(diff(chi(eta), eta))*(f(eta)+g(eta))-.7500000000*eta*(diff(chi(eta), eta)) = 0

 (5)
> 

Vc[2] := [.2, .3, .4]
> 

etainf := 1.85
> 

bcs := (D(f))(0) = k[1], (D(g))(0) = k[3], f(0) = 0, g(0) = 0, (D(theta))(0) = -Bi*(1-theta(0))/(1+c[4]*phi(0)), Nb*(D(phi))(0)*(1+c[6]*(2*phi(0)+1))+Nt*(D(theta))(0) = 0, chi(0) = 1, (D(f))(etainf) = k[2], (D(g))(etainf) = k[2], theta(etainf) = 0, phi(etainf) = 0, chi(etainf) = 0

(D(f))(0) = 0, (D(g))(0) = 0, f(0) = 0, g(0) = 0, (D(theta))(0) = -.5+.5*theta(0), 0.1e-4*(D(phi))(0)*(1.3+.6*phi(0))+0.1e-4*(D(theta))(0) = 0, chi(0) = 1, (D(f))(1.85) = 1, (D(g))(1.85) = 1, theta(1.85) = 0, phi(1.85) = 0, chi(1.85) = 0

 (6)
> 

dsys := {Eq1, Eq2, Eq3, Eq4, Eq5, bcs}
> 

for i to 3 do c[2] := Vc[2][i]; dsol[i] := dsolve(dsys, numeric, continuation = lambda); print(c[2]); print(dsol[i](0)) end do

.2

  

[eta = 0., chi(eta) = HFloat(1.0), diff(chi(eta), eta) = HFloat(3.888290578689045), f(eta) = HFloat(0.0), diff(f(eta), eta) = HFloat(0.0), diff(diff(f(eta), eta), eta) = HFloat(2.244199282192492), g(eta) = HFloat(0.0), diff(g(eta), eta) = HFloat(0.0), diff(diff(g(eta), eta), eta) = HFloat(2.244199282192492), phi(eta) = HFloat(-2.044191234673432), diff(phi(eta), eta) = HFloat(5.227515304629519), theta(eta) = HFloat(0.2317093657771352), diff(theta(eta), eta) = HFloat(-0.38414531711143246)]

  

.3

  

[eta = 0., chi(eta) = HFloat(1.0), diff(chi(eta), eta) = HFloat(4.148187853914835), f(eta) = HFloat(0.0), diff(f(eta), eta) = HFloat(0.0), diff(diff(f(eta), eta), eta) = HFloat(3.1086884419918364), g(eta) = HFloat(0.0), diff(g(eta), eta) = HFloat(0.0), diff(diff(g(eta), eta), eta) = HFloat(3.1086884419918364), phi(eta) = HFloat(-2.049332060722701), diff(phi(eta), eta) = HFloat(5.527786294980874), theta(eta) = HFloat(0.2216792480031605), diff(theta(eta), eta) = HFloat(-0.38916037599841974)]

  

.4

  

[eta = 0., chi(eta) = HFloat(0.9999999999999998), diff(chi(eta), eta) = HFloat(4.580796631072469), f(eta) = HFloat(0.0), diff(f(eta), eta) = HFloat(0.0), diff(diff(f(eta), eta), eta) = HFloat(5.687607599246298), g(eta) = HFloat(0.0), diff(g(eta), eta) = HFloat(0.0), diff(diff(g(eta), eta), eta) = HFloat(5.687607599246298), phi(eta) = HFloat(-2.0568809171520708), diff(phi(eta), eta) = HFloat(6.0203396482123575), theta(eta) = HFloat(0.20686299926628238), diff(theta(eta), eta) = HFloat(-0.39656850036685887)]

 (7)
> 

NULL

 

 

Download 3DAKc2w_-_Copy.mw

How to solve this PDE problem?...

faisal 15 Maple 16
pde numeric pdsolve
May 22 2016
1 4


> 

restart
> 

with(plots):
> 

NULL
> 

Nr := .2;

.2

  

1

  

0.5e-3

  

0.1e-2

  

1

  

0

 (1)
> 

PDE := {n*f(eta, xi)^(n-1)*`∂`(`#mscripts(mo("⁢"),none(),none(),none(),none(),none(),mn("2"))`)*f(eta, xi)/(`∂`(eta)*`#mscripts(mo("⁢"),none(),none(),none(),none(),none(),mn("2"))`) = diff(theta(eta, xi), eta)-Nr*(diff(phi(eta, xi), eta)), diff(phi(eta, xi), eta, eta)+(3/2)*Le*f(eta, xi)*(diff(phi(eta, xi), eta))+Nt*(diff(theta(eta, xi), eta, eta))/Nb = (1/2)*Le*xi*((diff(f(eta, xi), eta))*(diff(phi(eta, xi), xi))-(diff(phi(eta, xi), eta))*(diff(f(eta, xi), xi))), diff(theta(eta, xi), eta, eta)+Nb*(diff(phi(eta, xi), eta))*(diff(theta(eta, xi), eta))+(3/2)*f(eta, xi)*(diff(theta(eta, xi), eta))+Nt*(diff(theta(eta, xi)^2, eta)) = (1/2)*xi*((diff(f(eta, xi), eta))*(diff(theta(eta, xi), xi))-(diff(theta(eta, xi), eta))*(diff(f(eta, xi), xi)))}

Error, invalid input: diff received 0, which is not valid for its 2nd argument

  
> 

etainf := 1:
> 

IBC := {f(0, xi) = -(1/4)*xi, phi(0, xi) = 1, phi(etainf, xi) = 0, theta(0, xi) = 1, theta(etainf, xi) = 0};

{f(0, 0) = 0, phi(0, 0) = 1, phi(1, 0) = 0, theta(0, 0) = 1, theta(1, 0) = 0}

 (2)
> 

n := [.5, .8, 1.0, 1.5]

[.5, .8, 1.0, 1.5]

 (3)
> 

for i to 4 do n := L[i]; pds := pdsolve(PDE, IBC, numeric, spacestep = 1/10); p[i] := plots[display]([seq(pds:-plot(-u, t = (1/10)*j, y = 0 .. 6, legend = L[i]), j = 10)]) end do

L[1]

  

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same

  
> 

display({p[1], p[2], p[3], p[4]})

Error, (in plots:-display) expecting plot structures but received: {p[1], p[2], p[3], p[4]}

  
> 

NULL

NULL


Download non_newtonian_non_darcy.mw

hai All,

i have problem to soilve pde in the maple

can anyone suggest / idea to solve in maple?

Error in dsolve/numeric...

faisal 15 Maple
dsolve numeric bvp
January 26 2016
1 1

Hai everyone

may i ask why solution have an error?

hope i have an answer

r

 

NULL

> 

restart
> 

with(plots):
> 

Pr := 6.8:
> 

Eq1 := (101-100*lambda)*(diff(f(eta), `$`(eta, 3)))+f(eta)*(diff(f(eta), `$`(eta, 2)))+2*delta*theta(eta)+2*delta*Nc*gamma(eta)-2*delta*Nr*phi(eta);

(101-100*lambda)*(diff(diff(diff(f(eta), eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))+2*theta(eta)+2*gamma(eta)-2*phi(eta)

 (1)
> 

Eq2 := (101-100*lambda)*(diff(theta(eta), `$`(eta, 2)))+Pr*f(eta)*(diff(theta(eta), eta))+Pr*Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Pr*Nt*(diff(theta(eta), eta))^2;

(101-100*lambda)*(diff(diff(theta(eta), eta), eta))+6.8*f(eta)*(diff(theta(eta), eta))+3.40*(diff(theta(eta), eta))*(diff(phi(eta), eta))+3.40*(diff(theta(eta), eta))^2

 (2)
> 

Eq3 := (101-100*lambda)*(diff(phi(eta), `$`(eta, 2)))+Le*f(eta)*(diff(phi(eta), eta))+Nt*(diff(theta(eta), `$`(eta, 2)))/Nb;

(101-100*lambda)*(diff(diff(phi(eta), eta), eta))+.1*f(eta)*(diff(phi(eta), eta))+1.000000000*(diff(diff(theta(eta), eta), eta))

 (3)
> 

Eq4 := (101-100*lambda)*(diff(gamma(eta), `$`(eta, 2)))+Sc*s*(diff(theta(eta), `$`(eta, 2)))+Sc*f(eta)*(diff(gamma(eta), eta));

(101-100*lambda)*(diff(diff(gamma(eta), eta), eta))+.30*(diff(diff(theta(eta), eta), eta))+.6*f(eta)*(diff(gamma(eta), eta))

 (4)
> 

VBi := [10, 20, 30]:
> 

etainf := 5:
> 

bcs := f(0) = 0, (D(f))(0) = 0, (D(theta))(0) = -Bi*(1-theta(0)), phi(0) = 1, gamma(0) = 1, (D(f))(etainf) = 1, theta(etainf) = 0, phi(etainf) = 0, gamma(etainf) = 0;

f(0) = 0, (D(f))(0) = 0, (D(theta))(0) = -Bi*(1-theta(0)), phi(0) = 1, gamma(0) = 1, (D(f))(5) = 1, theta(5) = 0, phi(5) = 0, gamma(5) = 0

 (5)
> 

dsys := {Eq1, Eq2, Eq3, Eq4, bcs}:
> 

for i to 3 do Bi := VBi[i]; dsol[i] := dsolve(dsys, numeric, continuation = lambda); print(Bi); print(dsol[i](0)) end do

Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution

  
> 

NULL

NULL

 

Download soret.mw

 

 

Error in dsolve/numeric/bvp...

faisal 15 Maple
ode dsolve nonlinear
January 26 2016
1 4

i have run higer order nonlinear ode bvp

but cant solve the error

please help me

NULL

> 

restart
> 

with(plots)
> 

Pr := .71; beta := .5; alpha := .1; S := .1; Du := .1; Nb := .1; Nt := .1; Sc := .67; Sr := .1; omega := 1.0; Lb := 1.0; Pe := 1.0; delta := 1.0; Nc := 1.0; p := .1; q := 5; r := 5; s := 5; a := 1; b := 2; epsilon := .1
> 

Eq1 := (101-100*lambda)*(diff(f(eta), `$`(eta, 3)))-theta(eta)*beta*(diff(f(eta), `$`(eta, 2)))/(1+theta(eta)*beta)+(1+theta(eta)*beta)*f(eta)*(diff(f(eta), `$`(eta, 2)))-(1+theta(eta)*beta)*(diff(f(eta), eta))^2-(M-alpha)*(1+theta(eta)*beta)*(diff(f(eta), eta))

(101-100*lambda)*(diff(diff(diff(f(eta), eta), eta), eta))-.5*theta(eta)*(diff(diff(f(eta), eta), eta))/(1+.5*theta(eta))+(1+.5*theta(eta))*f(eta)*(diff(diff(f(eta), eta), eta))-(1+.5*theta(eta))*(diff(f(eta), eta))^2-(M-.1)*(1+.5*theta(eta))*(diff(f(eta), eta))

 (1)
> 

Eq2 := (1+epsilon*theta(eta))*(diff(theta(eta), `$`(eta, 2)))+f(eta)*(diff(theta(eta), eta))+epsilon*(diff(theta(eta), eta))^2+Pr*S*theta(eta)+Pr*Du*(diff(phi(eta), `$`(eta, 2)))+Pr*Nb*(diff(theta(eta), eta))*(diff(phi(eta), eta))+Pr*Nt*(diff(theta(eta), eta))^2

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta))+.171*(diff(theta(eta), eta))^2+0.71e-1*theta(eta)+0.71e-1*(diff(diff(phi(eta), eta), eta))+0.71e-1*(diff(theta(eta), eta))*(diff(phi(eta), eta))

 (2)
> 

Eq3 := (diff(phi(eta), `$`(eta, 2)))/Sc+f(eta)*(diff(phi(eta), eta))-omega*(diff(theta(eta), eta))*(diff(phi(eta), eta))-omega*(diff(theta(eta), `$`(eta, 2)))*phi(eta)-delta*phi(eta)+omega*Nc*(diff(theta(eta), `$`(eta, 2)))+Sr*(diff(theta(eta), `$`(eta, 2)))

1.492537313*(diff(diff(phi(eta), eta), eta))+f(eta)*(diff(phi(eta), eta))-1.0*(diff(theta(eta), eta))*(diff(phi(eta), eta))-1.0*(diff(diff(theta(eta), eta), eta))*phi(eta)-1.0*phi(eta)+1.10*(diff(diff(theta(eta), eta), eta))

 (3)
> 

Eq4 := diff(chi(eta), `$`(eta, 2))+Lb*f(eta)*(diff(chi(eta), eta))-Pe*(diff(phi(eta), eta))*(diff(chi(eta), eta))-Pe*(diff(phi(eta), `$`(eta, 2)))*chi(eta)

diff(diff(chi(eta), eta), eta)+1.0*f(eta)*(diff(chi(eta), eta))-1.0*(diff(phi(eta), eta))*(diff(chi(eta), eta))-1.0*(diff(diff(phi(eta), eta), eta))*chi(eta)

 (4)
> 

VM := [0., .5, 1.0]
> 

etainf := 9
> 

bcs := f(0) = 0, (D(f))(0) = p*(D@@2)(f)*0, theta(0) = 1+q*(D(theta))(0), phi(0) = 1+r*(D(phi))(0), chi(0) = 1+s*(D(chi))(0), D(f)*etainf = b/a, theta(etainf) = 0, phi(etainf) = 0, chi(etainf) = 0

f(0) = 0, (D(f))(0) = 0., theta(0) = 1+5*(D(theta))(0), phi(0) = 1+5*(D(phi))(0), chi(0) = 1+5*(D(chi))(0), 9*D(f) = 2, theta(9) = 0, phi(9) = 0, chi(9) = 0

 (5)
> 

dsys := {Eq1, Eq2, Eq3, Eq4, bcs}
> 

for i to 3 do M := VM[i]; dsol[i] := dsolve(dsys, numeric, continuation = lambda); print(M); print(dsol[i](0)) end do
> 

 
> 

 

 

  

How to solve this ODE BVP?...

faisal 15 Maple
ode numeric bvp
December 19 2015
0 1

using FDM or FEM rather than dsolve?

ode.docxode.docx

1 2 3 4 Page 3 of 4