initial guessing - for mixed boundary condition

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N Nithya
N Nithya 2022-9-5
回答： Sarthak 2023-9-13
f'''+(1/2)*f*f''+lamda*theta
theta''+pr*(1/2*f*theta'+f'*theta
with B.C f(eta) = 0,f'(eta) = delta*f''(eta) , theata(eta)=1+beta*theta'(eta) at eta = zero
f'(eta) = 1 ,theta(eta) = 0 as eta = infinity
close all
solinit = bvpinit(linspace(0,2),@exlinit );
options = bvpset('RelTol',1e-6);
sol = bvp4c(@convec,@bvp,solinit,options);
figure(1)
plot(sol.x,sol.y(4,:),'linewidth',1.5);
%plot(sol.x,sol.y(5,:),'--','linewidth',1.5);
hold on
function dy = convec(t,y)
lamda = 1;
Pr = 6.2;
dy(1) = y(2);
dy(2) = y(3);
dy(3) = -(1/2)*y(1)*y(3)+lamda*y(4);
dy(4) = y(5);
dy(5) = -(Pr)*(1/2*y(1)*y(5)+y(2)*y(4));
dy =[dy(1);dy(2);dy(3);dy(4);dy(5)];
end
function res = bvp(ya,yb)
delta = 0.5;
beta = 1;
res = [ya(1)-0
ya(2)-delta*ya(3)
yb(2)-1;
ya(4)-1-beta*ya(5);
yb(4)-0];
end
function v = exlinit(t)
v = [0
1
1-exp(-t)
1
exp(-t)];
end
the program is running but not getting correct one for example temperature profile ie y(4)
kindly give a suggestion for guessing a initial condition for the problem
  1 个评论
Torsten
Torsten 2022-9-5
From your equations, it should be
dy(3) = -(1/2)*y(1)*y(3)-lamda*y(4);
instead of
dy(3) = -(1/2)*y(1)*y(3)+lamda*y(4);

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回答（1 个）

Sarthak
Sarthak 2023-9-13
Hi N Nithya,
I understand you are looking for a way of initial guessing, but I found something else in the code which might help.
The equation for dy(3) should be:
dy(3) = -(1/2)*y(1)*y(3) - lamda*y(4)
The original equation, dy(3) = -(1/2)y(1)y(3) + lamday(4), is incorrect because the term lamday(4) should be negative.
The negative sign in front of the term lamda*y(4) is important because it ensures that the derivative of dy(3) is always negative. This is necessary because dy(3) represents the rate of change of y(3), and the rate of change of y(3) should always be negative when y(3) is increasing.
Hope this solves your query.

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