# ImplicitLNLMethods

From the paper:
*Implicit and Implicit-Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order*

The methods have a naming format of ( ‘number of stages’ `s`  ‘Linear Order’ `p` ’ Type.mat).  For example `2s2pDIRKLinear.mat` is a method with 2 stages and order of accuracy 2 for Linear problems and is has accuracy designed for Linear problems.  Each file contains the following pieces of information:

- s: the number of stages of the method
- p: the order of accuracy of the method
- r: the SSP coefficient of the method
- A: The Butcher Tableau for intermediate stages
- B: The Butcher Tableau for the reconstruction procedure
- alpha: From the Shu-Osher coefficient Matrix
- beta: From the Shu Osher coefficient Matrix
- v	: From the Shu Osher coefficient Matrix
 
Implementation of the scheme can be followed from any paper of SSP time Stepping methods.
The Co-optimized methods, which mention real or imag in their type, correspond to the methods which contain suboptimal SSP coefficients but try to optimize for better linear stability regions ( as presented in the paper). Note we only generated a few methods of this type they are methods which contain 5 stages of order 4 for linear problems, and order 3 for nonlinear problems.

Any questions about coefficients or need for more methods please contact Zachary Grant (zgrant@umassd.edu)