Advanced Search

Question: Boundary value problem

Question:Boundary value problem

madhavi 15 Maple
differential-equation dsolve numeric
January 02 2017
0

(1)How can i draw a graph by considering eta on x-axis and f'(eta),theta(eta)on y-axis in a single graph with respect to variatiation  in the parameter beta=0.01,0.1,1.0.. 

(2). how can i get different values of f'(eta) by varying values of eta .

> 

restart; with(plots); beta := 0.1e-1; Bi := 10; Pr := 3.0; L0 := 1; w := 0.2e-1
> 

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2+beta*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2+0.1e-1*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

 (1)
> 

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+beta*(F(eta)-(diff(f(eta), eta))) = 0

G(eta)*(diff(F(eta), eta))+F(eta)^2+0.1e-1*F(eta)-0.1e-1*(diff(f(eta), eta)) = 0

 (2)
> 

Eq3 := G(eta)*(diff(G(eta), eta))+beta*(f(eta)+G(eta)) = 0

G(eta)*(diff(G(eta), eta))+0.1e-1*f(eta)+0.1e-1*G(eta) = 0

 (3)
> 

Eq4 := H(eta)*F(eta)+H(eta)*(diff(G(eta), eta))+G(eta)*(diff(H(eta), eta)) = 0

H(eta)*F(eta)+H(eta)*(diff(G(eta), eta))+G(eta)*(diff(H(eta), eta)) = 0

 (4)
> 

Eq5 := (diff(theta(eta), eta, eta))/Pr+f(eta)*(diff(theta(eta), eta))+(2*H(eta)*beta*(1/3))*(thetap(eta)-theta(eta)) = 0

.3333333333*(diff(diff(theta(eta), eta), eta))+f(eta)*(diff(theta(eta), eta))+0.6666666667e-2*H(eta)*(thetap(eta)-theta(eta)) = 0

 (5)
> 

Eq6 := G(eta)*(diff(thetap(eta), eta))+L0*beta*(thetap(eta)-theta(eta)) = 0

G(eta)*(diff(thetap(eta), eta))+0.1e-1*thetap(eta)-0.1e-1*theta(eta) = 0

 (6)
> 

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(theta))(0) = -Bi*(1-theta(0)), (D(f))(5) = 0, F(5) = 0, G(5) = -f(5), H(5) = w, theta(5) = 0, thetap(5) = 0;

f(0) = 0, (D(f))(0) = 1, (D(theta))(0) = -10+10*theta(0), (D(f))(5) = 0, F(5) = 0, G(5) = -f(5), H(5) = 0.2e-1, theta(5) = 0, thetap(5) = 0

 (7)
> 

p := dsolve({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, numeric);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 14; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := eval(`dsolve/numeric/data/modules`[1]); solnproc := data:-Get("soln_procedure"); if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data:-Get("sysvars") elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data:-Get("soln_procedures")[0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[F(eta), G(eta), H(eta), f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), theta(eta), diff(theta(eta), eta), thetap(eta)]'[i] = res[i+1], i = 1 .. 9)] catch: error end try end proc

 (8)
> 

odeplot(p, [eta, f(eta)], 0 .. 5);

 
> 

odeplot(p, [eta, diff(f(eta), eta)], 0 .. 5);

 
> 

NULL
> 

odeplot(p, [eta, thetap(eta)], 0 .. 5);

 
> 

odeplot(p, [[eta, F(eta)], [eta, thetap(eta)]], 0 .. 5);

 
> 

``


 

Download from_net_(1).mw

 
Please Wait...