adaptburgers_mol.zip contains simple matlab codes that solve 1-D time-dependent Burgers' equation using method of lines with ode15s as time-stepping method and adaptive residual subsampling for radial basis functions in space.
T.A. Driscoll and A.R.H Heryudono
Adaptive Residual Subsampling Methods for Radial Basis Function Interpolation and Collocation Problems, Submitted to. Comput. Math. Appl.
The paper can be downloaded from :
Unzip the file, and run adaptburgers_mol.m
The codes can be modified to solve other 1-D nonlinear pdes such as Allen-Cahn, etc.
More codes can be downloaded from
I read through the code, very nice implementation