how to convert ode15 code into Runge kutta 4th order

CL= 1000;%pacing cycle length in ms

beats= 10;%number of beats in the simulation

options=[];%options for ode solver

for n=[1:beats]

[time X]=ode15s(@model,[0 CL],X0,options,1);

X0=X(size(X,1),:);

n %output beat number to the screen to monitor runtime progress

end

[James Tursa]

Ordinarily you could just replace ode15s with ode45, assuming your new problem isn't stiff. Or are you asking how to write your own RK4 code from scratch?

[Gur Pyari Rajput]

Thanks James Tursa.... I will try...

Answer 1

[prabhat kumar sharma]

Hi Gur,

You can simply use ode45 instead of ode15 if your new problem is not stiff or If you are willing to write your own RK4 so you can follow the below refrence.

% Given parameters
CL = 1000; % Pacing cycle length in ms
beats = 10; % Number of beats in the simulation
X0 = [...]; % Initial conditions, define according to your model

% RK4 parameters
dt = 1; % Time step in ms, choose according to desired accuracy

% Placeholder for model function
% Ensure your model function is defined as: dxdt = model(t, X, ...)
% where dxdt is the rate of change of your variables (the derivative),
% t is the current time, and X is the current state vector

for n = 1:beats
    time = 0:dt:CL; % Time vector for the current beat
    X = zeros(length(time), length(X0)); % Initialize state matrix
    X(1, :) = X0; % Set initial state
    
    for i = 1:(length(time)-1)
        % Calculate the four slopes
        k1 = dt * model(time(i), X(i, :)', 1);
        k2 = dt * model(time(i) + dt/2, X(i, :)' + k1/2, 1);
        k3 = dt * model(time(i) + dt/2, X(i, :)' + k2/2, 1);
        k4 = dt * model(time(i) + dt, X(i, :)' + k3, 1);
        
        % Update the state
        X(i+1, :) = X(i, :) + (k1 + 2*k2 + 2*k3 + k4)'/6;
    end
    
    X0 = X(end, :); % Prepare initial condition for the next beat
    disp(['Beat number: ', num2str(n)]); % Output beat number to monitor progress
end