4.5.5 pde.solvers.explicit module

Defines an explicit solver supporting various methods.

class EulerSolver(pde, *, backend='auto', adaptive=False, tolerance=0.0001)[source]

Bases: AdaptiveSolverBase

Explicit Euler solver.

Parameters:

  • pde (PDEBase) – The partial differential equation that should be solved

  • backend (str) – Determines how the function is created. Accepted values are ‘numpy` and ‘numba’. Alternatively, ‘auto’ lets the code decide for the most optimal backend.

  • adaptive (bool) – When enabled, the time step is adjusted during the simulation using the error tolerance set with tolerance.

  • tolerance (float) – The error tolerance used in adaptive time stepping. This is used in adaptive time stepping to choose a time step which is small enough so the truncation error of a single step is below tolerance.

name = 'euler'
class ExplicitSolver(pde, scheme='euler', **kwargs)[source]

Bases: AdaptiveSolverBase

Various explicit PDE solvers.

Parameters:

  • pde (PDEBase) – The partial differential equation that should be solved

  • backend (str) – Determines how the function is created. Accepted values are ‘numpy` and ‘numba’. Alternatively, ‘auto’ lets the code decide for the most optimal backend.

  • adaptive (bool) – When enabled, the time step is adjusted during the simulation using the error tolerance set with tolerance.

  • tolerance (float) – The error tolerance used in adaptive time stepping. This is used in adaptive time stepping to choose a time step which is small enough so the truncation error of a single step is below tolerance.

  • scheme (Literal['euler', 'runge-kutta', 'rk', 'rk45'])

name = 'explicit'
class RungeKuttaSolver(pde, *, backend='auto', adaptive=False, tolerance=0.0001)[source]

Bases: AdaptiveSolverBase

Explicit Runge-Kutta PDE solver of order 5(4).

Parameters:

  • pde (PDEBase) – The partial differential equation that should be solved

  • backend (str) – Determines how the function is created. Accepted values are ‘numpy` and ‘numba’. Alternatively, ‘auto’ lets the code decide for the most optimal backend.

  • adaptive (bool) – When enabled, the time step is adjusted during the simulation using the error tolerance set with tolerance.

  • tolerance (float) – The error tolerance used in adaptive time stepping. This is used in adaptive time stepping to choose a time step which is small enough so the truncation error of a single step is below tolerance.

name = 'runge-kutta'