How can I write these functions to the press

[Walter Roberson]

I am not sure what you mean by "to the press" ?

[Bilal Ates]

Sorry I typed it wrong. I want to write in matlab

[Bilal Ates]

clc;                                               % Clears the screen
clear all;
h=0.25;                                             % step size
x = 0:h:1;                                         % Calculates upto y(4)
y = zeros(1,length(x)); 
z = ???
y(0) = 2;                                          % initial condition
z(0) = 4;
F_xy = ??????????                 % change the function as you desire
F_xz = ??????????
for i=1:(length(x)-1)                              % calculation loop
    k_1 = F_xy(x(i),y(i));
    k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);
    k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));
    k_4 = F_xy((x(i)+h),(y(i)+k_3*h));
    y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;  % main equation
end

Answer 1

[Ameer Hamza]

You can use ode45() to solve such a system of ODEs.

ic = [2; 4];
xspan = [0 1];
[x, Q] = ode45(@odeFun, xspan, ic);
y_sol = Q(:,1);
z_sol = Q(:,2);
plot(x, Q);
legend({'y', 'z'}, 'FontSize', 16);

function dQdx = odeFun(x, Q)
    % Q(1) <=> y, Q(2) <=> z
    
    y = Q(1);
    z = Q(2);
    dydx = -2*y + 4*exp(-x) + exp(-1000*z^2);
    dzdx = -y*z^2/3;
    dQdx = [dydx; dzdx];
end