Differential Equation Solving System: Difference between revisions

Revision as of 18:05, 17 January 2016

AKA: Differential Equation Solver.
Example(s):
- Taylor Series Method System.
- Euler Method System.
- Runge-Kutta Method System, that applies a Runge-Kutta algorithm.
- Predictor-Corrector Method System.
- Adams-Bashforth Method System, that applies an Adams-Bashforth algorithm..
- Adam-Moulton Method System, that applies an Adam-Moulton algorithm..
- Milne-Simpson Method System, that applies a Milne-Simpson algorithm..
- a PDE System.
- an ODE System.
See: Differential Equation.

@@ Line 4: / Line 4: @@
 ** [[Taylor Series Method System]].
 ** [[Euler Method System]].
-import math
-import matplotlib.pyplot as plt
-\#\ Initial conditions
-y0 = 2.0
-\# Time step and final time
-dt = 1.0 # days
-tf = 364 .0 # days
-\# Empty lists to hold the time and solution
-tt = [ ]
-yy = [ ]
-\# Append initial values
-tt.append (0.0)
-yy . append (y0)
-\# Parameters of our equation
-a = 0.01
-omega = 2.0*math.pi/365.0
-\# Iteration
-while tt [−1] <= tf :
-r = a*yy[−1]*(1+math . sin(omega*tt[ − 1 ]))
-yy.append(yy[−1]+ r*dt)
-tt.append (tt[−1]+dt)
-plt.figure(1)
-plt.plot(tt,yy,'.')
-plt.xlabel('Time[days]')
-plt.ylabel('Rats[rats]')
-plt.title('Euler Solution')
-plt.show( )
 ** [[Runge-Kutta Method System]], that applies a [[Runge-Kutta algorithm]].
 ** [[Predictor-Corrector Method System]].