Sat Feb  5 17:50:33 2022

odefun_test():
  Python version: 3.6.9
  Demonstrate the use of the mpmath multiple precision function
  odefun() to solve some simple ordinary differential equations (ODE)

odefun_test01():
  odefun() solves the ODE: y = y
  Exact solution is y(x) = exp(x)

  Use 15 digit arithmetic:
(0.0, 1.0, 1.0)
(1.0, 2.71828182845905, 2.71828182845905)
(2.5, 12.1824939607035, 12.1824939607035)

  Use 50 digit arithmetic:
(0.0, 1.0, 1.0)
(1.0, 2.7182818284590452353602874713526624977572470937, 2.7182818284590452353602874713526624977572470937)
(2.5, 12.182493960703473438070175951167966183182767790063, 12.182493960703473438070175951167966183182767790063)

odefun_test02():
  ODE: y = y

  Use 15 digit arithmetic and vector form of ODE.
([1.0], 1.0)
([2.71828182845905], 2.71828182845905)
([12.1824939607035], 12.1824939607035)

  Use 50 digit arithmetic and vector form of ODE.
([1.0], 1.0)
([2.7182818284590452353602874713526624977572470937], 2.7182818284590452353602874713526624977572470937)
([12.182493960703473438070175951167966183182767790063], 12.182493960703473438070175951167966183182767790063)

odefun_test03():
  Solve nonlinear ODE: y = x*sin(y)

  Use 15 digit arithmetic.
(2.87255666284091, 2.87255666284091)
(3.14158520028345, 3.14158520028345)
(3.14159265358979, 3.14159265358979)

  Use 50 digit arithmeticE.
(2.8725566628409117191074779550054627306546626704065, 2.8725566628409117191074779550054627306546626704065)
(3.1415852002834491156243575719681632794591593184052, 3.1415852002834491156243575719681632794591593184052)
(3.1415926535897932384622576333099101006405659308118, 3.1415926535897932384622576333099101006405659308118)

odefun_test04():
  Solve autonomous nonlinear ODE: y = (1+x**2)/(1+x**3)
  Compare solution to quadrature result.
odefun() solution at 2 pi: 0.72128263801696
quadrature at 2 pi:        0.72128263801696

odefun_test05():
  ODE: y0 = -y1
       y1 =  y0
[1.0, 0.0]
[1.0, 0.0]
---
[0.54030230586814, 0.841470984807897]
[0.54030230586814, 0.841470984807897]
---
[-0.801143615546934, 0.598472144103957]
[-0.801143615546934, 0.598472144103957]
---
[-0.839071529076452, -0.54402111088937]
[-0.839071529076452, -0.54402111088937]
---

odefun_test():
  Normal end of execution.
Sat Feb  5 17:51:04 2022