How to make a function that uses Runge-Kutta Method

Hello, I am trying to create a function that can take in a function and solve it using Runge-Kutta's method. For example, I should be able to input dy/dx = x+y , y(0) = 1 and get an answer from the funtion. I've been working with this equation for a while, I just cannnot figure out how to format this into a function. Here is what I have.

function [OutputX,OutputY] = FunctionBeta_Executor(h,x,y,FunctionA)

h=1.5; % step size

x = 0:h:3; % Calculates upto y(3)

y = zeros(1,length(x));

y(1) = 5; % initial condition

FunctionA = F_xy; % change the function as you desire

for i=1:(length(x)-1)

i=1:(length(x)-1) % calculation loop

k1 = F_xy(x(i),y(i));

k2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k1);

k3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k2));

k4 = F_xy((x(i)+h),(y(i)+k_3*h));

y(i+1) = y(i) + (1/6)*(k1+2*k2+2*k3+k4)*h; % main equation

end

end

% For example, FunctionA might be dy/dx = x+y , with inital conditions y(0)=1.

Answer 1

[Sulaymon Eshkabilov]

Hi,

Here is the corrected code:

function [x, y] = FunctionBeta_Executor(F)
% Note that F function expression is defined via Function Handle: F = @(x, y)(x+y)               
% change the function as you desire
h=0.15;                                             % step size (smaller step size gives more accurate solutions)
x = 0:h:3;                                          % x space
y = zeros(1,length(x));                             % Memory allocation
y(1) = 5;                                           % initial condition

for i=1:(length(x)-1)                             
% i=1:(length(x)-1)                              % calculation loop
    k1 = F(x(i),y(i));
    k2 = F(x(i)+0.5*h,y(i)+0.5*h*k1);
    k3 = F((x(i)+0.5*h),(y(i)+0.5*h*k2));
    k4 = F((x(i)+h),(y(i)+k3*h));
    y(i+1) = y(i) + (1/6)*(k1+2*k2+2*k3+k4)*h;  % main equation
end
figure, plot(x, y)  % To see the solution results
end

Now you can test the above function with the followings, e.g. in the command window:

>> F = @(x, y)(x+y);
>> [OutputX,OutputY] = FunctionBeta_Executor(F);

Good luck.

[OvercookedRamen]

Thank you so much! You're a life saver.

[Sulaymon Eshkabilov]

It is a pleasure that I could be of some help.