Applications: Longitudinal oscillating chains; PDEs

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

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+# 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