Gabriel samaila

MaplePrimes Activity


These are questions asked by Gabriel samaila

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

 

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

 

 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

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

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

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