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Updated 13 Sep 2006
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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.
Reference:
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 :
http://www.math.udel.edu/php/deptapps/techrept.php?year=2006
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
Alfa Heryudono (2021). Adaptive residual subsampling for Radial Basis Functions (https://www.mathworks.com/matlabcentral/fileexchange/11101-adaptive-residual-subsampling-for-radial-basis-functions), MATLAB Central File Exchange. Retrieved .
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I read through the code, very nice implementation