b1g3


b1g3, a C code which solves one or more ordinary differential equations (ODE) using the (implicit) b1g3 method, with a version of fsolve() handling the associated nonlinear equation, and using a fixed time step.

Each b1g3 step requires the solution of an implicit nonlinear equation. A corresponding function has been devised, called fsolve_b1g3(), which carries out the iterative solution process.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

b1g3 is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

b1g3_test

c_ode_solver, a C code which solves one or more differential equations (ODE) using a method of a particular order, either explicit or implicit. Some methods require a nonlinear equation solver. Some methods used a fixed stepsize, while others adapt the stepsize based on an error estimate.

fsolve, a C code which solves systems of nonlinear equations, inspired by the fsolve() function in minpack(), with special interfaces fsolve_bdf2(), fsolve_be() and fsolve_tr() for handling systems associated with implicit ODE solvers of type b1g3, bdf2, backward Euler, midpoint, or trapezoidal.

Reference:

  1. Catalin Trenchea, John Burkardt,
    Refactorization of the b1g3 rule,
    Applied Mathematics Letters,
    Volume 107, September 2020.

Source Code:


Last revised on 28 November 2025.