acbook-time-integration
Code examples for time integration chapter of book, "Astrochemical modelling: practical aspects of microphysics in numerical simulations," edited by Stefano Bovino and Tommaso Grassi.
These codes are grouped into the following categories:
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Running examples: each module should include functions that implement the IVP right-hand side, the RHS Jacobian (in dense, sparse, and Jacobian-vector product formats), the reference solution, and a function to return the eigenvalues of the Jacobian. The module should also specify the initial condition, time interval, and any relevant parameters as module-level global variables
- example1.py : functions for the "non-stiff" running example.
- example2.py : functions for the "stiff" running example
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Shared utilities:
- implicit_solver.py : module that defines an "ImplicitSolver" class, whose objects implement a modified Newton iteration with either dense, sparse, GMRES, or preconditioned GMRES inner linear solver.
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Simple time-steppers:
- forward_euler.py : basic forward Euler time stepper
- backward_euler.py : basic backward Euler time stepper
- erk.py : basic explicit Runge--Kutta time stepper, that accepts Butcher table as input
- dirk.py : basic diagonaly-implicit Runge--Kutta time stepper, that accepts Butcher table as input
- explicit_lmm.py : basic explicit linear multistep time stepper, that accepts LMM coefficients as input
- implicit_lmm.py : basic implicit linear multistep time stepper, that accepts LMM coefficients as input
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Advanced drivers:
- example1_comparison.py : script that runs various explicit methods on example 1, including built-in adaptive solvers
- example2_comparison.py : script that runs various implicit methods on example 2, including built-in adaptive solvers