# BVP PROBLEM how can we take 'c' in x-axis(continuous range.[-1.3:0.02:-1.1]) and to find f"(0)

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MINATI on 3 Mar 2019
Commented: MINATI on 7 Mar 2019
function main
S = 1; c = -1.25; Pr = 0.7; n = -0.8;
x = [3 -1];
x1 = fsolve(@solver, x);
function F = solver(x)
[t, u] = ode45(@equation,[0,5], [S, c, x(1), 1, x(2)]);
F = [u(end, 2)-1 u(end, 4)];
figure(1)
plot(t, u(:,2));
hold on
end
function dy = equation(t, y)
dy = zeros(5,1);
dy(1) = y(2);
dy(2) = y(3);
dy(3) = y(2)^2 - y(1) * y(3) - 1;
dy(4) = y(5);
dy(5) = Pr * (n * y(2) * y(4) - y(1) * y(5));
end
end

Torsten on 4 Mar 2019
Is f = y(1) ?
MINATI on 4 Mar 2019
Dear Torsten
yes f = y(1)
Sorry for seeing late

Torsten on 4 Mar 2019
function main
S = 1; c = [-1.3:0.02:-1.1]; Pr = 0.7; n = -0.8;
sol = zeros(numel(c),1);
x = [3 -1];
for i = 1:numel(c)
c_actual = c(i);
x1 = fsolve(@solver, x);
sol(i) = x1(1);
x = x1;
end
plot(c,sol)
function F = solver(x)
[t, u] = ode45(@equation,[0,5], [S, c_actual, x(1), 1, x(2)]);
F = [u(end, 2)-1 , u(end, 4)];
end
function dy = equation(t, y)
dy = zeros(5,1);
dy(1) = y(2);
dy(2) = y(3);
dy(3) = y(2)^2 - y(1) * y(3) - 1;
dy(4) = y(5);
dy(5) = Pr * (n * y(2) * y(4) - y(1) * y(5));
end
end

Torsten on 6 Mar 2019
Can you elaborate ?
MINATI on 6 Mar 2019
I am working on this attached paper. For reference you can follow:
Want to solve Eq.(11)(12) with B.Cs (13)(14)
In Fig. (2-5), in X-axis c/a is taken.
In other figs., dual solution concept is used i.e if we change x = [3 -1]; as anything like x = [5 -2]; or any other, we will get SECOND solution.
MINATI on 7 Mar 2019