Solving for two variables using 4th order Runga Kutta Method

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Caroline Kenemer
Caroline Kenemer 2022-4-23
回答： Torsten 2022-4-23
I need to use a 4th order Runga Kutta method to find variables u and t.
du/dr = f(r,t)
dt/dr = f(r,t,u)
u(j+1) = +
where
and
where

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回答（1 个）

Torsten
Torsten 2022-4-23
Define your functions for du/dr and dt/dr in the line f = @(r,y) ... and adapt the settings in the calling program according to your needs.
rstart = 0.0;
rend = 1.0;
h = (rend - rstart)/20;
R = (rstart:h:rend).';
Y0 = [1 -1];
B = 4;
f = @(r,y) [y(2) -exp(-B*r)-y(1)+5*exp(-2*r)-2*exp(-(B+2)*r)+exp(-B*r)+r];
Y = runge_kutta_RK4(f,R,Y0);
plot(R,Y)
function Y = runge_kutta_RK4(f,R,Y0)
N = numel(R);
n = numel(Y0);
Y = zeros(N,n);
Y(1,:) = Y0;
for i = 2:N
r = R(i-1);
y = Y(i-1,:);
h = R(i) - R(i-1);
k0 = f(r,y);
k1 = f(r+0.5*h,y+k0*0.5*h);
k2 = f(r+0.5*h,y+k1*0.5*h);
k3 = f(r+h,y+k2*h);
Y(i,:) = y + h/6*(k0+2*k1+2*k2+k3);
end
end

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