Forward euler - a system of 4 ode
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I am trying to program in matlab a code to excute forward euler. I have these DE:
x'(t)=u
y'(t)=v
u'(t)=-kx*u*V
v'(t)=-g-ky(v*V)
where kx,ky and g are constants and V=sqrt(u^2+v^2)
The first thing that I have done is that I have called:
w_1'=x'
w_2'=y'
w_3'=u'
w_4'=v'
so I can express the 4 system of DE in terms of w:
w_3
w_4
-kx*w_3+sqrt((w_3)^2+(w_4)^2)
-g-ky*w_4*(sqrt((w_3)^2+(w_4)^2)
Now to the MATLAB code:
x0 = 0;
N = 16000;
h = 2./N;
kx=0.020;
ky=0.065;
g=9.81;
x_i = [0 ; 1.5; 19*cos(45); 19*sin(45)]; % initialconditons
for i = 1:N;
x_n = x0 + (i-1).*h;
diff=[x_n;x_n;-kx*(x_n*sqrt((x_n).^2+(x_n).^2));-g-ky*x_n*sqrt((x_n).^2+(x_n).^2)];
e= x_i + h.*diff; %euluerforward
end
I am not sure if I have done it right, because my answers are almost similiar to my initialconditions?
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