surf plot is required

A = 1; M = 1; Da = 0.1; L = 0.1; Pr = 1; Nb = 0.1; Nt = 0.5; s = 0.5; Le = 2; Kc = 1;B = 0.5;Lv = linspace(-2,2,100);
for M = [0 1 2]
    for i = 1:length(Lv)
        L = Lv(i);
        ODE = @(x,y) [ y(2);  y(3);  y(2)^2 - y(1)*y(3) - A^2 + (M+Da)*(y(2)-A) - L*y(4);  
            y(5);  -Pr*( y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4) )
            y(7);  -Le*Pr*(y(1)*y(7) - Kc*y(6)) + (Nt/Nb)*Pr*( y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4) )];
        BC = @(ya,yb)[ya(1);  ya(2)-1;  ya(5)-B*(ya(4)-1); Nb*ya(7)+Nt*ya(5); yb(2)-A; yb([4,6])]; xa = 0; xb = 6; 
        x = linspace(xa,xb,100); solinit = bvpinit(x,[0 1 0 1 0 1 0]); sol = bvp5c(ODE,BC,solinit);  S = deval(sol,x);
        figure(1),surf(x,Lv,[1;1]*S(2,:));hold on;xlabel('\bfx','Color','blue'); ylabel('\bfL','Color','blue');
        zlabel '\bfS(2,:)';
    end
end

Error using surf
Data dimensions must agree.

%%% Want to draw surf plot of S(2,:) with 'x' as x-axis variation, 'L' as y-axis variation

Answer 1

[Voss]

Like this?

A = 1; M = 1; Da = 0.1; L = 0.1; Pr = 1; Nb = 0.1; Nt = 0.5; s = 0.5; Le = 2; Kc = 1;B = 0.5;
xa = 0; xb = 6;
Lv = linspace(-2,2,100);
x = linspace(xa,xb,100);
S_all = zeros(numel(Lv),numel(x));
for M = [0 1 2]
    for i = 1:numel(Lv)
        L = Lv(i);
        ODE = @(x,y) [ y(2);  y(3);  y(2)^2 - y(1)*y(3) - A^2 + (M+Da)*(y(2)-A) - L*y(4);
            y(5);  -Pr*( y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4) )
            y(7);  -Le*Pr*(y(1)*y(7) - Kc*y(6)) + (Nt/Nb)*Pr*( y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4) )];
        BC = @(ya,yb)[ya(1);  ya(2)-1;  ya(5)-B*(ya(4)-1); Nb*ya(7)+Nt*ya(5); yb(2)-A; yb([4,6])];
        solinit = bvpinit(x,[0 1 0 1 0 1 0]);
        sol = bvp5c(ODE,BC,solinit);
        S = deval(sol,x);
        S_all(i,:) = S(2,:);
    end
    figure()
    surf(x,Lv,S_all);
    hold on;
    xlabel('\bfx','Color','blue');
    ylabel('\bfL','Color','blue');
    zlabel('\bfS(2,:)');
    title(sprintf('M = %d',M));
end

Warning: Unable to meet the tolerance without using more than 1428 mesh points.
The last mesh of 294 points and the solution are available in the output argument.
The maximum error is 256.798, while requested accuracy is 0.001.

Warning: Unable to meet the tolerance without using more than 1428 mesh points.
The last mesh of 294 points and the solution are available in the output argument.
The maximum error is 85.7775, while requested accuracy is 0.001.

Answer 2

[Mrutyunjaya Hiremath]

To create the surface plot for the given code, you can use the MATLAB 'surf' function inside the loop. However, you need to be careful about the input arguments to the 'surf' function to ensure that the data is correctly plotted.

• Here's the modified code with the surf plot:

A = 1; M = 1; Da = 0.1; Pr = 1; Nb = 0.1; Nt = 0.5; s = 0.5; Le = 2; Kc = 1; B = 0.5;
Lv = linspace(-2, 2, 100);

figure(1);
hold on;
xlabel('\bfx', 'Color', 'blue');
ylabel('\bfL', 'Color', 'blue');
zlabel('\bfS(2,:)');

for M = [0, 1, 2]
    for i = 1:length(Lv)
        L = Lv(i);
        ODE = @(x, y) [ y(2);  y(3);  y(2)^2 - y(1)*y(3) - A^2 + (M + Da)*(y(2) - A) - L*y(4);  
                        y(5);  -Pr*(y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4))
                        y(7);  -Le*Pr*(y(1)*y(7) - Kc*y(6)) + (Nt/Nb)*Pr*(y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4))];
        
        BC = @(ya, yb) [ya(1);  ya(2) - 1;  ya(5) - B*(ya(4) - 1); Nb*ya(7) + Nt*ya(5); yb(2) - A; yb([4, 6])];
        xa = 0; xb = 6; 
        x = linspace(xa, xb, 100);
        solinit = bvpinit(x, [0, 1, 0, 1, 0, 1, 0]);
        sol = bvp5c(ODE, BC, solinit);
        S = deval(sol, x);
        
        surf(x, Lv(i)*ones(size(x)), [1; 1]*S(2, :));
    end
end

hold off;

• This code should create a surface plot showing the variation of S(2,:) with respect to x and L for different values of M. The surf function is used to plot the data, and we use Lv(i)*ones(size(x)) to create a meshgrid for the surf plot, with Lv(i) repeated for the entire x range.

[MINATI PATRA]

@ Mrutyunjaya Hiremath

After running the code the following ERROR is coming:

Error using surf

Data dimensions must agree.

Error (line 13)

surf(x, Lv(i)*ones(size(x)), [1; 1]*S(2, :));

[Mrutyunjaya Hiremath]

clc;
close all;
clear all;

A = 1; M = 1; Da = 0.1; Pr = 1; Nb = 0.1; Nt = 0.5; s = 0.5; Le = 2; Kc = 1; B = 0.5;
Lv = linspace(-2, 2, 100);

figure(1);
hold on;
xlabel('\bfx', 'Color', 'blue');
ylabel('\bfL', 'Color', 'blue');
zlabel('\bfS(2,:)');

for M_val = [0, 1, 2]
    for i = 1:length(Lv)
        L = Lv(i);
        ODE = @(x, y) [ y(2);  y(3);  y(2)^2 - y(1)*y(3) - A^2 + (M_val + Da)*(y(2) - A) - L*y(4);
            y(5);  -Pr*(y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4))
            y(7);  -Le*Pr*(y(1)*y(7) - Kc*y(6)) + (Nt/Nb)*Pr*(y(1)*y(5) + Nb*y(5)*y(7) + Nt*y(5)^2 + s*y(4))];
        
        BC = @(ya, yb) [ya(1);  ya(2) - 1;  ya(5) - B*(ya(4) - 1); Nb*ya(7) + Nt*ya(5); yb(2) - A; yb([4, 6])];
        xa = 0; xb = 6;
        x = linspace(xa, xb, 100);
        solinit = bvpinit(x, [0, 1, 0, 1, 0, 1, 0]);
        sol = bvp5c(ODE, BC, solinit);
        S = deval(sol, x);
        
        % Use meshgrid to create a 2D grid of x and Lv(i) values
        [X, Y] = meshgrid(x, Lv(i)*ones(size(x)));
        
        % Reshape [1; 1]*S(2, :) to match the size of the grid
        Z = repmat([1]*S(2, :), size(X, 1), 1);
        
        surf(X, Y, Z);
    end
end

hold off;

% Enable interactive rotation of the 3D plot
rotate3d on;

% Set the initial view to a 45-degree rotation
view(45, 45);