Math6321-codes

Codes for in-class collaboration for the course: Numerical Solution of ODEs (MATH 6321) at Southern Methodist University, for the Fall 2023 semester.

These codes require a modern Python installation.

Note: the c++ branch includes implementations of the same solvers, but in C++, and that use the "Armadillo" C++ library (http://arma.sourceforge.net) for vectors, matrices, and linear solvers.

Codes are grouped according to type:

• initial_demo -- simple demonstration scripts showing the use of Python for mathematical calculations and plotting.
• shared -- reusable ImplicitSolver class, to be used by implicit ODE methods.
• newton -- test driver to show use of ImplicitSolver.
• forward_euler -- simple IVP "evolution" routine, based on the simplest IVP solver. Basic approach for timestep adaptivity. Contains two classes, ForwardEuler (fixed-step evolution) and AdaptEuler (adaptive-step evolution).
• simple_implicit -- simple implicit ODE solver classes, BackwardEuler and Trapezoidal, showing use of the ImplicitSolver class for implicit ODE methods.
• explicit_one_step -- higher-order explicit, one-step, ODE integration methods, containing the Taylor2 and ERK classes.
• implicit_one_step -- higher-order implicit, one-step, ODE integration methods, containing the DIRK and IRK classes.
• linear_multistep -- higher-order explicit and implicit multi-step ODE integration methods, containing the classes ExplicitLMM and ImplicitLMM.
• bvp -- two-point boundary-value problem solvers.

Daniel R. Reynolds
Mathematics @ SMU