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Codes for R K 4th order simultaneous methods for n ODE

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ARKA
ARKA 2023-6-22
评论： ARKA 2023-9-21
I want to solve n ODE by using RK 4 simultaneous method. please help me with proper code with example. atleast 4 equations.
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ARKA
ARKA 2023-6-22
yea I am writing by my self, and thsts why I want to see some examples. with more number of equations.
Torsten
Torsten 2023-6-22
Ran in:
tstart = 0.0;
tend = 1.0;
h = 0.01;
T = (tstart:h:tend).';
Y0 = [1 -1];
Y = runge_kutta_RK4(@f,T,Y0);
plot(T,Y)
grid on
function Y = runge_kutta_RK4(f,T,Y0)
N = numel(T);
n = numel(Y0);
Y = zeros(N,n);
Y(1,:) = Y0;
for i = 2:N
t = T(i-1);
y = Y(i-1,:);
h = T(i) - T(i-1);
k0 = f(t,y);
k1 = f(t+0.5*h,y+k0*0.5*h);
k2 = f(t+0.5*h,y+k1*0.5*h);
k3 = f(t+h,y+k2*h);
Y(i,:) = y + h/6*(k0+2*k1+2*k2+k3);
end
end
function dy = f(t,y)
B = 4;
dy = [y(2) -exp(-B*t)-y(1)+5*exp(-2*t)-2*exp(-(B+2)*t)+exp(-B*t)+t];
end

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Mudit Kumar Bhugari

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