Problema 3:

prob3.m

function [z]=prob3(f,df,a,b,y,h)x=a:h:b;n=length(x);z=[x(1) y];for i=1:n-1y=y+h*feval(f,x(i),y)+(h^2)/2*feval(df,x(i),y);z=[z ;x(i+1) y];end

Evaluando:

>> f=inline('(x.*x-1).*y');df=inline('((2*x+(x*x-1).^2).*y)');z=prob3(f,df,0,1,1,0.25)

z = 0 1.0000 0.2500 0.7813 0.5000 0.6318 0.7500 0.5442 1.0000 0.5134

Problema 4:

a) Con Euler:

Prob4.m

function [z]=prob4(f,a,b,y,h)x=a:h:b;n=length(x);z=[x(1) y];for i=1:n-1y=y+h*feval(f,x(i),y);z=[z ;x(i+1) y];end

Probando:

f=inline('4*exp(0.8*x)-0.5*y');z=prob4(f,0,3,2,0.1)

b) Con RK-2:

rk2.m

function [z]=rk2(f,a,b,y,h)x=a:h:b;n=length(x);z=[x(1) y];for i=1:n-1k1=h*feval(f,x(i),y(i));k2=f*feval(f,x(i+1),y(i)+k1);y(i+1)=y(i)+0.5*(k1+k2);z=[z ;x(i+1) y(i)];end

Probando

f=inline('4*exp(0.8*x)-0.5*y');

z=eulerp(f,0,3,2,0.1)

Z= 0 2.0000 0.1000 2.3000 0.2000 2.6183 0.3000 2.9568 0.4000 3.3175 0.5000 3.7024 0.6000 4.1140 0.7000 4.5548 0.8000 5.0273 0.9000 5.5345 1.0000 6.0796 1.1000 6.6658 1.2000 7.2969 1.3000 7.9767 1.4000 8.7096 1.5000 9.5000 1.6000 10.3531 1.7000 11.2741 1.8000 12.2689 1.9000 13.3437 2.0000 14.5054 2.1000 15.7613 2.2000 17.1195 2.3000 18.5885 2.4000 20.1777 2.5000 21.8972 2.6000 23.7579 2.7000 25.7718 2.8000 27.9517 2.9000 30.3114 3.0000 32.8661