// TP 2 : Activité 1 

function dy=f(t,y)
dy=-y+t+1
endfunction

function gradient(f,a)
t=linspace(-a,a,11)
t=t(1:10)
y=t
ft=ones(10,10)
fy=feval(t,y,f)
champ(t,y,ft,fy,rect=[-a -a a a])
xtitle("Champ de tangentes","t","y")
endfunction

function [t,y]=euler(f,t0,y0,tmax,n)
t=linspace(t0,tmax,n+1)
yn=y0
y=y0
h=(tmax-t0)/n
for i=1:n
    y=[y yn+h*f(t(i),yn)]
    yn=yn+h*f(t(i),yn)
end
endfunction

function [t,y]=runge2(f,t0,y0,tmax,n)
t=linspace(t0,tmax,n+1)
yn=y0
y=y0
h=(tmax-t0)/n
for i=1:n
    v1=f(t(i),yn)
    yn=yn+h*f(t(i)+h/2,yn+h*v1/2)
    y=[y yn]
end
endfunction

function [t,y]=runge4(f,t0,y0,tmax,n)
t=linspace(t0,tmax,n+1)
yn=y0
y=y0
h=(tmax-t0)/n
for i=1:n
    v1=f(t(i),yn)
    v2=f(t(i)+h/2,yn+v1*h/2)
    v3=f(t(i)+h/2,yn+v2*h/2)
    v4=f(t(i)+h,yn+h*v3)
    yn=yn+h*(v1+2*v2+2*v3+v4)/6
    y=[y yn]
end
endfunction