Differential Equation Solving System: Difference between revisions

Revision as of 13:36, 14 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.

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 ** [[Taylor Series Method System]].
 ** [[Euler Method System]].
-Python Implementation in [[Euler Solver]]
-import math\\
-import ma t p lo t lib . p y p lo t a s p l t
-# I n i t i a l c o n d i t i o n s
-y0 = 2 .0
-# Time s t e p and f i n a l t i me
-dt = 1 .0 # days
-t f = 3 6 4 .0 # days
-# Empty l i s t s t o h o ld t h e t i me and s o l u t i o n
-t t = [ ]
-yy = [ ]
-# Append i n i t i a l v a l u e s
-t t . append ( 0 . 0 )
-yy . append ( y0 )
-# Paramet ers o f our e q u a t i o n
-a = 0 .0 1
-omega = 2 .0 *math . p i / 3 6 5 .0
-# I t e r a t i o n
-while t t [ − 1] < = t f :
-r = a * yy [ − 1] * (1+math . s i n ( omega *t t [ − 1 ]) )
-yy . append ( yy[ −1]+ r *dt )
-t t . append ( t t [ −1]+ dt )
-p l t . f i g u r e ( 1 )
-p l t . p lo t ( t t , yy , '. ')
-p l t . x l a b e l ( 'Time [ days ] ')
-p l t . y l a b e l ( 'Rats [ r a t s ] ')
-p l t . t i t l e ( 'Euler S o lu t io n ')
-p l t . show ( )
 ** [[Runge-Kutta Method System]], that applies a [[Runge-Kutta algorithm]].
 ** [[Predictor-Corrector Method System]].