scripts/alpaca23 partial differential equation.LACE

   1 # Solving partial differential equations by descretizing space
   2 # This is an adoption of the application note “alpaca_23” from Anabrid [https://analogparadigm.com/downloads/alpaca_23.pdf]
   3 # THAT only has 5 integrators, thus we have to reduce the number of elements
   4 #
   5 # u_0 = delta_t
   6 # u''_1 = u_0 - 2*u_1 + u_2
   7 # u''_2 = u_1 - 2*u_2 + u_3
   8 # u_3 = 0
   9
  10 coefficient(1): f1 # fix to 0.2 to get 2 for the integration
  11 coefficient(2): f2 # fix to 0.2 to get 2 for the integration
  12 coefficient(5): 1 -> delta_t
  13 u_0 = delta_t
  14 coefficient(6): 0 -> u_3
  15
  16 iintegrate u_0, 10*:-f1u_1, u_2 -> -u'_1 # input is u''_1
  17 iintegrate -u'_1 -> u_1
  18 invert u_1 -> -u_1
  19 -u_1 * f1 -> -f1u_1
  20
  21 iintegrate u_1, 10*:-f2u_2, u_3 -> -u'_2 # input is u''_2
  22 iintegrate -u'_2 -> u_2
  23 invert u_2 -> -u_2
  24 -u_2 * f2 -> -f2u_2
  25
  26 output(x): u_1
  27 output(y): u_2