ppp
Euler’s Method MATLAB Program. function[]=m_euler h=0.1; f=@(x,y) x.^2+y; x=0:h:1; y(1)=1; n=length(x); yp(1)=y; maxit=10; for i=2:n yp(i)=y(i-1)+h*f(x(i-1),y(i-1)); s(i,1)=yp(i); for j=2:maxit s(i,j) = y(i-1)+(h/2)*(f(x(i-1),y(i-1))+f(x(i),s(i,j-1))); if abs(s(i,j)-s(i,j-1))<10^(-6) y(i)=s(i,j); break end end end fprintf('Appr. sol. y(%f)=%f',x(end),y(end)) plot(x,yp,'m--') hold on plot(x,y,'r--') hold on u=dsolve('Dy=x^2+y','y(0)=1','x'); u=eval(u); plot(x,u,'b--') legend('Appr. sol. by Euler','Appr. sol. by Modified Euler','Exact sol.') end dsolve and ode45 y=dsolve('Dy=3*x+y/2','y...