RKLab provides a suite of Matlab files that implement adaptivestep explicit and implicit RungeKutta methods. This software is designed for instructional use and has been implemented to be easily understood and modified. As a result, certain efficiencyrelated optimizations have been omitted. We currently provide three classes of methods: (a) explicit RungeKutta (ERK), (b) diagonallyimplicit RungeKutta (DIRK), and (c) fully implicit RungeKutta (IRK). In addition to these three classes of methods, we provide a large number of Butcher tables (over 70), holding the coefficients for existing methods in each of these three categories. For ERK and DIRK methods, time step adaptivity is enabled for methods with embeddings (most of the included ERK and DIRK methods include embeddings). For IRK methods, time step adaptivity is performed using a Richardson error estimate (cost of 3 solves per step), but leverages the additional cost through using the Richardson extrapolation for the time step solution. All three classes of methods may be run in socalled "fixedstep mode", wherein the solver will take steps of a usersupplied magnitude. This mode is currently required for ERK and DIRK methods without embeddings. In addition to these sets of solvers, we provide three example problems that may be used to test different methods, and that may be used as a template for creating new problems. These test problems include: (a) a nonstiff variant of the Van der Pol oscillator (twocomponent nonlinear ODE system). (b) a stiff Brusselator problem (threecomponent nonlinear ODE system), and (c) a PDE variant of the Brusselator problem (twocomponent nonlinear PDE system).
Source
RKLab /
Filename  Size  Date modified  Message 

42 B


added hgignore file


852 B


Initial import


1.3 KB


Initial import


471 B


Initial import


469 B


Initial import


470 B


Initial import


858 B


Initial import


1.3 KB


Initial import


370 B


Initial import


453 B


Initial import


1.1 KB


Initial import


853 B


Initial import


1.7 KB


Updated solve_IRK to allow time step adaptivity, using Richardson error estimator (and subsequent Richardson extrapolation).


37.6 KB


Updated header comments to better describe methods in one place.


2.4 KB


Updated example problem drivers to use adaptivestep IRK solver as well.


2.5 KB


Updated example problem drivers to use adaptivestep IRK solver as well.


2.9 KB


Updated example problem drivers to use adaptivestep IRK solver as well.


343 B


Initial import


413 B


Initial import


897 B


Initial import


2.2 KB


Updated Newton solver to input separate solution and residual tolerances; solvers currently use the same tolerance for both.


9.1 KB


Updated Newton solver to input separate solution and residual tolerances; solvers currently use the same tolerance for both.


7.7 KB


Removed damping from Newton solver and renamed appropriately.


12.0 KB


Updated Newton solver to input separate solution and residual tolerances; solvers currently use the same tolerance for both.
