what is the meaning of error "Index exceeds the number of array elements. Index must not exceed 8."

function Latest_code

%%

for Pr = [1 2 3 4]

% Define constants

M = 0.5;

B = 0.5;

C = 0.2;

A = 0.1;

R = 0.1;

E = 0.1;

K = 0.5;

W = 0.1;

N = 0.1;

T = 0.3;

Q = 0.1;

N1 = 0.1;

N2 = 0.1;

S = 0.1;

d = 1;

m = 1;

E1 = 0.1;

Pe = 0.2;

S1 = 0.1;

M1 = 0.1;

O = 0.1;

% Defining initial guess

solinit = bvpinit(linspace(0, 2, 50), [1 0 0 0 1 1 1 1]);

% Solving the boundary value problem

sol = bvp4c(@bvpexam2, @bcexam2, solinit);

x = sol.x;

y = sol.y;

% Plotting of velocity

figure(2)

plot(x, y(4, :), 'linewidth', 1)

ylim([0 1])

xlim([0 9])

hold on

xlabel('\eta', 'FontWeight', 'bold', 'FontSize', 16)

ylabel('\theta(\eta)', 'FontWeight', 'bold', 'FontSize', 16)

end

% System of first order ODEs

function yvector = bvpexam2(~, y)

yy1 = (1 / (1 + (1 / B))) * (2 * y(2) * y(2) - y(1) * y(3) + M * y(2) + K * y(2) - W * (y(4) - N * y(7) - R));

yy2 = -(1 / (((4 / 3) * R) + 1)) * (Pr * (y(1) * y(5) - y(2) * y(4) - T * y(2) + Q * y(4) + N1 * y(8) * y(5) + N2 * y(5) * y(5) + E * (1 + 1 / B) * y(3) * y(3) + (E * y(2) * y(2)) * (M + K)));

yy3 = -S * (y(1) * y(8) - y(2) * y(7) - C * y(2) - A * y(7) * ((1 + d * y(4)) ^ m) * exp(-E1 / (1 + d * y(4)))) - (N2 / N1) * y(6);

yy4 = (Pe * (y(9) * (y(10) + O) + y(11) * y(8))) - (S1 * ((y(11) - y(10)) * y(1))) + (S1 * M1 * y(2));

yvector = [ y(2); y(3); yy1; y(5); yy2; y(8); yy3 ; y(11); yy4 ];

end

% Residual of the boundary conditions

function residual = bcexam2(y0, yinf)

residual = [y0(1)- 1; y0(2) - 1; y0(4) - 1 +T ; y0(7)-1+C ; y0(10)-1+M1 ; yinf(2); yinf(4); yinf(7); yinf(10)];

end

end

Answer 1

[Aquatris]

it means the size of y variable is 8 abd you are trying to get 9th 10th 11th index of the y vector. This is because your initial solution, defined in sol_init variable consist of only 8 elements, where it should be 11. So a simple fix is you fix this line:

%solinit = bvpinit(linspace(0, 2, 50), [1 0 0 0 1 1 1 1]);

Then you had some syntax error in bcexam2() function. When you put space between x +T in an array element, matlab can think it is a 2 element vector. You should use paranthesis or no space when you define that way.

And lastly, since your solution is 11x1 vector, you should modify your bcexam2 function to provide 11x1 vector instead of 9x1. I cannot solve this one as I have no idea what equation you are trying to solve.

Latest_code

Error using bvparguments (line 99)
Error in calling BVP4C(ODEFUN,BCFUN,SOLINIT):
The derivative function ODEFUN should return a column vector of length 11.

Error in bvp4c (line 119)
bvparguments(solver_name,ode,bc,solinit,options,varargin);

Error in solution>Latest_code (line 31)
sol = bvp4c(@bvpexam2, @bcexam2, solinit);

function Latest_code
%% 
for Pr = [1 2 3 4]
    % Define constants
    
    M = 0.5;
    B = 0.5;
    C = 0.2;
    A = 0.1;
    R = 0.1;
    E = 0.1;
    K = 0.5;
    W = 0.1; 
    N = 0.1; 
    T = 0.3; 
    Q = 0.1; 
    N1 = 0.1;
    N2 = 0.1; 
    S = 0.1; 
    d = 1; 
    m = 1; 
    E1 = 0.1;
    Pe = 0.2; 
    S1 = 0.1; 
    M1 = 0.1; 
    O = 0.1; 
    % Defining initial guess
    solinit = bvpinit(linspace(0, 2, 50), [1 0 0 0 1 1 1 1 1 1 1]);
    % Solving the boundary value problem
    sol = bvp4c(@bvpexam2, @bcexam2, solinit);
    x = sol.x;
    y = sol.y;
    % Plotting of velocity
    figure(2)
    plot(x, y(4, :), 'linewidth', 1)
    ylim([0 1])
    xlim([0 9])
    hold on
    xlabel('\eta', 'FontWeight', 'bold', 'FontSize', 16)
    ylabel('\theta(\eta)', 'FontWeight', 'bold', 'FontSize', 16)
end
% System of first order ODEs
    function yvector = bvpexam2(~, y)
        yy1 = (1 / (1 + (1 / B))) * (2 * y(2) * y(2) - y(1) * y(3) + M * y(2) + K * y(2) - W * (y(4) - N * y(7) - R));
        yy2 = -(1 / (((4 / 3) * R) + 1)) * (Pr * (y(1) * y(5) - y(2) * y(4) - T * y(2) + Q * y(4) + N1 * y(8) * y(5) + N2 * y(5) * y(5) + E * (1 + 1 / B) * y(3) * y(3) + (E * y(2) * y(2)) * (M + K)));
        yy3 = -S * (y(1) * y(8) - y(2) * y(7) - C * y(2) - A * y(7) * ((1 + d * y(4)) ^ m) * exp(-E1 / (1 + d * y(4)))) - (N2 / N1) * y(6);
        yy4 = (Pe * (y(9) * (y(10) + O) + y(11) * y(8))) - (S1 * ((y(11) - y(10)) * y(1))) + (S1 * M1 * y(2));
        yvector = [ y(2); y(3); yy1; y(5); yy2; y(8); yy3 ; y(11); yy4 ];
    end
% Residual of the boundary conditions
    function residual = bcexam2(y0, yinf)
        residual = [(y0(1)- 1); (y0(2) - 1); (y0(4) - 1 +T) ; (y0(7)-1+C) ; (y0(10)-1+M1) ; yinf(2); yinf(4); yinf(7); yinf(10)];
    end
end