Take the first half of the original number and append that half's reverse to that half to get a palindrome. Include the middle digit separately between the forward and reverse if an odd number of digits. Lower the middle digit or two of that created palindrome if necessary to make sure the palindrome is less than or equal to the number. Use that palindrome, and subtract from the original number; then continue this process working on what remains each time, until there is nothing left:

 314159265353562951413 
 5416336145 
 36263 
 22 
 3 

    5   open "palinsum.txt" for output as #2

   10   dim Pal(30)

   20   Num$="314159265358979323846"

   30   N=val(Num$)

   40    gosub *Palinate(1)

   50    print Pal(1)+Pal(2)+Pal(3)+Pal(4)+Pal(5)

   60   close #2

  999   end

 1010   *Palinate(Wh)

 1015   P$=left(Num$,ceil(len(Num$)/2)):P1$=P$

 1020   for I=floor(len(Num$)/2) to 1 step -1

 1030      P$=P$+mid(Num$,I,1)

 1040   next

 1050   if val(Num$)-val(P$)<0 then

 1060    :P$=cutspc(str(val(P1$)-1))

 1070    :for I=floor(len(Num$)/2) to 1 step -1

 1080       :P$=P$+mid(Num$,I,1)

 1090    :next

 1100   :endif

 1150   Pal(Wh)=val(P$)

 1160   Num$=cutspc(str(val(Num$)-val(P$)))

 1170   if val(Num$)=0 then

 1180     :for I=1 to Wh

 1190        :print Pal(I):print #2,Pal(I)

 1200     :next

 1210   :else

 1220     :gosub *Palinate(Wh+1)

 1230   :endif

 1260   return