how to convert ode15 code into Runge kutta 4th order

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Gur Pyari Rajput
Gur Pyari Rajput 2021-7-22
回答： prabhat kumar sharma 2024-6-4
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
  2 个评论
James Tursa
James Tursa 2021-7-22
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?

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回答（1 个）

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

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