[Analog_Engine.git] / scripts / alpaca23 partial differential equation.LACE

# 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
Commit	Line	Data
56968557 P	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