Advanced Search

Gabriel samaila

35 Reputation

4 Badges

6 years, 120 days
Contact Gabriel samaila

MaplePrimes Activity


These are questions asked by Gabriel samaila

Ordinary differential equations...

Gabriel samaila 35 Maple 16
ode dsolve numeric
February 14 2019
1 21

Hi guys,

This is the first time of solving partial differential equation, can some please help me point out some errows in my code. 
 

> 

restart
> 

ODEs := `<,>`(diff(v(y), y, y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, diff(theta(y), y, y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, diff(phi(y), y, y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(theta(y), y, y)+(diff(theta(y), y))/y)/Nb = 0)

ODEs := Matrix(3, 1, {(1, 1) = diff(diff(v(y), y), y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, (2, 1) = diff(diff(theta(y), y), y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, (3, 1) = diff(diff(phi(y), y), y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(diff(theta(y), y), y)+(diff(theta(y), y))/y)/Nb = 0})

 (1)
> 

BCs := `<,>`(phi(eta) = 1, v(eta) = 1, theta(eta) = 1, phi(1) = 0, theta(1) = 0, v(1) = 0)

BCs := Matrix(6, 1, {(1, 1) = phi(eta) = 1, (2, 1) = v(eta) = 1, (3, 1) = theta(eta) = 1, (4, 1) = phi(1) = 0, (5, 1) = theta(1) = 0, (6, 1) = v(1) = 0})

 (2)
> 

param_names := [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr];

[eta, Ha, Ec, Nt, Nb, Re, Sc, Pr]

 (3)
> 

pdSolve := subs(_P = param_names, proc ({ eta::realcons := .5, Ha::realcons := 1, Sc::realcons := .8, Nt::realcons := .1, Nb::realcons := .1, Re::realcons := 2, Ec::realcons := 0.1e-1, Pr::realcons := 10 }) userinfo(1, Solve, `~`[`=`](param_names, _P)); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, _P)), numeric) end proc);

proc ({ Ec::realcons := 0.1e-1, Ha::realcons := 1, Nb::realcons := .1, Nt::realcons := .1, Pr::realcons := 10, Re::realcons := 2, Sc::realcons := .8, eta::realcons := .5 }) userinfo(1, Solve, `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])), numeric) end proc

 (4)
> 

infolevel[Solve] := 1:

Fig. 3 (changing values of Ha):

> 

P:= Ha:
vals:= [1, 5, 10, 20]:
sols:= [seq(Solve(P= v), v= vals)]:
colors:= [red, green, blue]:
for F in [v,theta,phi](y) do
   print(plots:-display(
      [seq(
         plots:-odeplot(sols[k], [y,F], color= colors[k], legend= [P= vals[k]]),
         k= 1..nops(vals)
      )],
      labeldirections= [horizontal,vertical]
   ))
od:

Error, pdeplot is not a command in the plots package

  
> 

``


 

Download chapter5.mw

 

multiple plots in single layout...

Gabriel samaila 35 Maple
differential-equation homework multiple
November 22 2018
1 2

Hi guys;

can one please show me how to plot graphs in on layout. i want like soundalgekar2004-deka.pdf using this code

variable.mw
 

> 

restart
> 

with*plots; -1; ode1 := diff(f(eta), eta, eta, eta)-(diff(theta(eta), eta))*(diff(f(eta), eta, eta))/(theta(eta)-R)-(theta(eta)-R)*f(eta)*(diff(f(eta), eta, eta))/(2*R) = 0

diff(diff(diff(f(eta), eta), eta), eta)-(diff(theta(eta), eta))*(diff(diff(f(eta), eta), eta))/(theta(eta)-R)-(1/2)*(theta(eta)-R)*f(eta)*(diff(diff(f(eta), eta), eta))/R = 0

 (1)
> 

ode2 := diff(theta(eta), eta, eta)-N*pr*(diff(f(eta), eta))*theta(eta)+(1/2)*pr*f(eta)*(diff(theta(eta), eta)) = 0

diff(diff(theta(eta), eta), eta)-N*pr*(diff(f(eta), eta))*theta(eta)+(1/2)*pr*f(eta)*(diff(theta(eta), eta)) = 0

 (2)
> 

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(38) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(38) = 0

 (3)
> 

fixedparameter := [pr = 0.2e-1, N = 1];

[pr = 0.2e-1, N = 1]

 (4)
> 

ode3 := eval(ode1, fixedparameter);

diff(diff(diff(f(eta), eta), eta), eta)-(diff(theta(eta), eta))*(diff(diff(f(eta), eta), eta))/(theta(eta)-R)-(1/2)*(theta(eta)-R)*f(eta)*(diff(diff(f(eta), eta), eta))/R = 0

 (5)
> 

bcs2 := theta(38) = 0, theta(0) = 1;

theta(38) = 0, theta(0) = 1

 (6)
> 

ode4 := eval(ode2, fixedparameter);

diff(diff(theta(eta), eta), eta)-0.2e-1*(diff(f(eta), eta))*theta(eta)+0.1000000000e-1*f(eta)*(diff(theta(eta), eta)) = 0

 (7)
> 

L := [2, 10, 15];

[2, 10, 15]

 (8)
> 

``
> 

for k to 3 do sol_All := dsolve(eval({bcs1, bcs2, ode3, ode4}, R = L[k]), [f(eta), theta(eta)], numeric, output = listprocedure); Y_sol || k := rhs(sol_All[5]); YP_sol || k := -rhs(sol_All[6]); ftheta || k := rhs(sol_All[3]); pftheta || k := -rhs(sol_All[4]) end do:
> 

for k to 3 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do;

2, [HFloat(1.0000000000000002), HFloat(0.07429586344532203)]

  

10, [HFloat(1.0000000000000007), HFloat(0.06509471738660902)]

  

15, [HFloat(0.9999999999999997), HFloat(0.06453272061469233)]

 (9)
> 

NULL
> 

NULL
> 

  plot( [ seq((Y_sol||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((ftheta||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((pftheta||j)(eta), j = 1..3)],
         eta = 0 .. 6,
         labels = [eta, fprime(eta)],
         axes = boxed
      );

 

 

 

 
> 

NULL
> 

``


 

Download variable.mw

 

3rd order differential equations...

Gabriel samaila 35 Maple
syntax homework differential-equations
October 09 2018
3 20

 Hi guys,

I dont know much about maple, please looking for someone to help me check this maple code as to why it is not running sign.mw . The ode is copied from singh2000-thermometer.pdf.

Thank you for your help

boundary value problem...

Gabriel samaila 35 Maple
September 30 2018
1 1

Hi all,

can some one please help me check the  mapple file.AZIZ.mw i copied from the the paper by abdul Aziz with reference [doi:10.1016/j.cnsns.2008.05.003] .

Thank you for your help

Please I need some one to help me with c...

Gabriel samaila 35 Maple 16
May 19 2018
3 27

Helo, guys, i am a beginner here I want solve a system of first order differential equation using RK4. Please I need help please.

1 2 Page 2 of 2