Hi guys. In the task, it is necessary to calculate by the Euler method with the initial condition y(x0)=y0 , [a;b] wiith epsilon 0.001.
I have a function, but it only works correctly if y^1
For example, when f=x^(-2)*y^3 will be an error function S = sym(x, n, a) and the program stops
euler('x^(-2)*y^3',[1 2],[1 4], 50, 0.001)
Maybe you can help me? What could be the problem?
function [] = euler( f,X0,AB,n0,eps )
x0=X0(1);
y0=X0(2);
a=AB(1);
b=AB(2);
dx=(b-a)/n0;
X(1)=x0;
Y(1)=y0;
for i=1:1:n0
syms x y
y0=y0+subs(subs(f,x,x0),y,y0)*dx;
x0=x0+dx;
X(i+1)=x0;
Y(i+1)=y0;
end
dx=dx/2;
x0=X0(1);
y0=X0(2);
X1(1)=x0;
Y1(1)=y0;
for i=1:1:2*n0
y0=y0+subs(subs(f,x,x0),y,y0)*dx;
x0=x0+dx;
X1(i+1)=x0;
Y1(i+1)=y0;
end
maax=max(abs(Y-Y1(1:2:end)));
Y1_=Y1;
x0=X0(1);
y0=X0(2);
figure(1)
hold on
grid on
plot(X,Y,'r');
plot(X1,Y1,'g');
m=0;
while (maax>eps)
m=m+1;
dx=dx/2;
X2(1)=x0;
Y2(1)=y0;
n=(b-a)/dx;
for i=1:1:n
y0=y0+subs(subs(f,x,x0),y,y0)*dx;
x0=x0+dx;
X2(i+1)=x0;
Y2(i+1)=y0;
end
maax=max(Y1_-Y2(1:2:end));
Y1_=Y2;
end
if m==0
fprintf('There is not enough accuracy for making 2 graphics\n');
else
plot(X2,Y2,'b');
end
for i=2:n+1
fprintf('x = %f\ty = %f\n',X2(i),Y2(i));
end
fprintf('It took %i pieces of fragmintation \n',n)
end
