Advanced Search

Question: Not able to solve the equation and How to obtain triple solution

Question:Not able to solve the equation and How to obtain triple solution

Madhukesh J K 140 Maple 17
ode dsolve numeric differential-equations bvp shooting-method
December 07 2020
0

I'm trying to solve the problem which is published in the research article. The paper is attached. 

This work done with the help of shooting technique in maple 18

1.Is it possible to solve in maple 17

2. How to obtain the triple soln

3. How to implement Shooting technique

Please anyone help me to get this 

 

restart:

with(plots):

eq1 := (1+K)*(diff(f(eta), `$`(eta, 3)))+f(eta)*(diff(f(eta), `$`(eta, 2)))+K*(diff(g(eta), eta))-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta)) = 0;

(1+K)*(diff(diff(diff(f(eta), eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))+K*(diff(g(eta), eta))-2*(diff(f(eta), eta))^2-M*(diff(f(eta), eta)) = 0

 (1)

eq2 := (1+(1/2)*K)*(diff(g(eta), `$`(eta, 2)))+f(eta)*(diff(g(eta), eta))-3*g(eta)*(diff(f(eta), eta))-2*K*g(eta)-K*(diff(f(eta), `$`(eta, 2))) = 0;

(1+(1/2)*K)*(diff(diff(g(eta), eta), eta))+f(eta)*(diff(g(eta), eta))-3*g(eta)*(diff(f(eta), eta))-2*K*g(eta)-K*(diff(diff(f(eta), eta), eta)) = 0

 (2)

eq3 := (1+(4/3)*Rd)*(diff(theta(eta), `$`(eta, 2)))/Pr+f(eta)*(diff(theta(eta), eta))+Nb*(diff(chi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2 = 0;

(1+(4/3)*Rd)*(diff(diff(theta(eta), eta), eta))/Pr+f(eta)*(diff(theta(eta), eta))+Nb*(diff(chi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2 = 0

 (3)

eq4 := diff(chi(eta), `$`(eta, 2))+Sc*f(eta)*(diff(chi(eta), eta))+Nt*(diff(theta(eta), `$`(eta, 2)))/Nb = 0;

diff(diff(chi(eta), eta), eta)+Sc*f(eta)*(diff(chi(eta), eta))+Nt*(diff(diff(theta(eta), eta), eta))/Nb = 0

 (4)

bcs := f(0) = S, (D(f))(0) = -1, g(0) = -m*((D^2)(f))(0), (D(theta))(0) = -A*(1-theta(0)), chi(0) = 1+delta*(D(chi))(0), (D(f))(10) = 0, g(10) = 0, theta(10) = 0, chi(10) = 0;

f(0) = S, (D(f))(0) = -1, g(0) = -m*(D(f))(0)^2, (D(theta))(0) = -A*(1-theta(0)), chi(0) = 1+delta*(D(chi))(0), (D(f))(10) = 0, g(10) = 0, theta(10) = 0, chi(10) = 0

 (5)

params := [K = .1, S = 2.1257, m = .5, Pr = 2, Nb = .3, Nt = .5, Sc = 2, Rd = .5, delta = .1, A = 5];

[K = .1, S = 2.1257, m = .5, Pr = 2, Nb = .3, Nt = .5, Sc = 2, Rd = .5, delta = .1, A = 5]

 (6)

sol := dsolve(eval([eq1, eq2, eq3, eq4, bcs], params), numeric, output = listprocedure, maxmesh = 5000)

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 10, got 9

  

``


 

Download Triple.mw
Please Wait...