# Solving partial differential equations by descretizing space
# This is an adoption of the application note “alpaca_23” from Anabrid [https://analogparadigm.com/downloads/alpaca_23.pdf] 
# THAT only has 5 integrators, thus we have to reduce the number of elements
#
# u_0 = delta_t 
# u''_1 = u_0 - 2*u_1 + u_2 
# u''_2 = u_1 - 2*u_2 + u_3 
# u_3 = 0

coefficient(1): f1 # fix to 0.2 to get 2 for the integration
coefficient(2): f2 # fix to 0.2 to get 2 for the integration
coefficient(5): 1 -> delta_t
u_0 = delta_t
coefficient(6): 0 -> u_3

iintegrate u_0, 10*:-f1u_1, u_2 -> -u'_1 # input is u''_1
iintegrate -u'_1 -> u_1
invert u_1 -> -u_1
-u_1 * f1 -> -f1u_1

iintegrate u_1, 10*:-f2u_2, u_3 -> -u'_2 # input is u''_2
iintegrate -u'_2 -> u_2
invert u_2 -> -u_2
-u_2 * f2 -> -f2u_2

output(x): u_1
output(y): u_2