Differential Equation Solving System

A Differential Equation Solving System is an equation solving system that can apply a differential equation solving algorithm to solve a differential equation solving task.

• AKA: Differential Equation Solver.
• Example(s):
  • Taylor Series Method System.
  • Euler Method System.

import math import matplotlib . pyplot as plt

1. Initial conditions

y0 = 2.0

1. Time step and final time

dt = 1.0 # days tf = 364 .0 # days

1. Empty lists to hold the time and solution

tt = [ ] yy = [ ]

1. Append initial values

tt.append (0.0) yy . append (y0)

1. Parameters of our equation

a = 0.01 omega = 2.0*math.pi/365.0

1. 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.
  • 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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