#
euler

**euler**,
a Python code which
solves one or more ordinary differential equations (ODE)
using the forward Euler method.

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Licensing:

The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.

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Languages:

**euler** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a FreeFem++ version and
a MATLAB version and
an Octave version and
a Python version and
an R version.

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Related Data and Programs:

backward_euler,
a Python code which
solves one or more ordinary differential equations (ODE)
using the backward Euler method.

leapfrog,
a Python code which
uses the leapfrog method to solve a second order ordinary
differential equation (ODE) of the form y''=f(t,y).

midpoint,
a Python code which
solves one or more ordinary differential equations (ODE)
using the (implicit) midpoint method.

midpoint_explicit,
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solves one or more ordinary differential equations (ODE)
using the (explicit) midpoint method, also called the
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midpoint_fixed,
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solves one or more ordinary differential equations (ODE)
using the (implicit) midpoint method, using a simple fixed-point
iteration to solve the nonlinear equation.

rk4,
a Python code which
applies the fourth order Runge-Kutta (RK) algorithm to estimate the
solution of an ordinary differential equation (ODE) at the next time
step.

rkf45,
a Python code which
implements the Runge-Kutta-Fehlberg (rkf) solver
for the solution of a system of ordinary differential equations (ODE).

trapezoidal,
a Python code which
solves one or more ordinary differential equations (ODE)
using the trapezoidal method.

trapezoidal_fixed,
a Python code which
solves one or more ordinary differential equations (ODE)
using the (implicit) trapezoidal method, using a fixed
point method to handle the implicit system.

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Source Code:

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Last revised on 29 April 2021.
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