#Sowmya Srinivasan hw17.txt 27 March 2014

#SIrec(L,Ini,f,m,n) inputs lists L,Ini, expression f in variable m, and n , 
#and outputs solution to 
#a(n)=L[1]*a(n-1)+L[2]*a(n-2)+ ... + L[-1]*a(n-nops(L))+f(n) 

SIrec:=proc(L,Ini,f,m,n) local i:
option remember:

if nops(L)<>nops(Ini) then
	print(Ini, L, `should be lists of the SAME length `):
	RETURN(FAIL):
fi:

if n<0 then
	0:
elif n<nops(Ini) then
	Ini[n+1]:
else
	add(L[i]*SIrec(L,Ini,f,m,n-i),i=1..nops(L) ) + subs(m=n,f): 
fi:

end : 


###################################


dIBVP:=proc(L,Ini,Fini,f,n,N) local eq,var,a,i:

if nops(L)<>nops(Ini)+nops(Fini) then
	RETURN(FAIL):
fi:

var:={seq(a[i],i=0..N)}:

eq:={seq(a[i]=Ini[i+1],i=0..nops(Ini)-1),
     seq(a[N-i]=Fini[i+1],i=0..nops(Fini)-1)}:

eq:=
eq union
{seq(a[i]-add(L[j]*a[i-j],j=1..nops(L))-subs(n=i,f), 
i=nops(L)..N)}:

var:=solve(eq,var):

if var=NULL then
	RETURN(FAIL):
else
	subs(var,[seq(a[i],i=0..N)]):
fi:

end: