same value for first and second solution
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function newfypAmir
format long g
%Define all parameters
global Pr A C M K SS
M = 1;
K = 1;
A = 3;
C = -12;
Pr = 0.5;
SS = 0;
%Boundary layer thickness & stepsize
etaMin = 0;
etaMax1 = 15;
etaMax2 = 12; %15, 10
stepsize1 = etaMax1;
stepsize2= etaMax2;
%%%%%%%%%%%%%%%%%%%%%% First solution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1), @OdeInit1);
sol = bvp4c(@OdeBVP, @OdeBC, solinit, options);
eta = linspace (etaMin, etaMax1, stepsize1);
y = deval (sol, eta);
%Displaying the output for first solution
fprintf('\nFirst solution:\n');
fprintf('f" = %7.9f\n',y(3));
fprintf('f` = %7.9f\n',y(2));
fprintf('theta = %7.9f\n',y(4));
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%% Second solution %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10);
solinit = bvpinit (linspace (etaMin, etaMax2, stepsize2), @OdeInit2);
sol = bvp4c (@OdeBVP, @OdeBC, solinit, options);
eta = linspace (etaMin, etaMax2, stepsize2);
y = deval (sol, eta);
%Displaying the output for second solution
fprintf('\nSecond solution:\n');
fprintf('f" = %7.9f\n',y(3));
fprintf('f` = %7.9f\n',y(2));
fprintf('theta = %7.9f\n',y(4));
fprintf('\n');
%Define the ODE function
function ff = OdeBVP(~, y, Pr, M, K, A, C, SS)
global Pr M K A C SS
ff = [
y(2)
y(3)
( y(2)*y(2) - y(1)*y(3) - K*(1-y(2)) - M*M*(1-y(2)) - 1 ) / Pr
y(5)
-1*y(1)*y(5)
];
%Define the boundary condition
function res = OdeBC(ya, yb, A, C, SS)
global A C SS
res = [
ya(1)-SS
ya(2)-C-A*ya(3)
ya(4)-1
yb(2)-1
yb(4)];
%Setting the initial guess for first solution
function v = OdeInit1 (~, A, C, SS)
global A C SS
v = [0.5
0
0
0
0];
%Setting the initial guess for second solution
function v1 = OdeInit2 (x, A, C, SS)
global A C SS
v1 = [exp(-x)
exp(-x)
exp(-x)
exp(-x)
exp(-x)];
1 Comment
Ganesh
on 29 Nov 2023
In the lines of code where you are printing the solution, you have printed y(2), y(3) and y(4), whereas y is a matrix.
Kindly ensure that you are trying to access the right matrix column.
Thank you,
Ganesh S
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