MATLAB code for RBF-PUM solvers for convection diffusion problems
These MATLAB codes are released to support reproducible research for the numerical results in the manuscript
-
A radial basis function partition of unity collocation method for convection–diffusion equations arising in financial applications
. In Journal of Scientific Computing, volume 64, pp 341-367, 2015. (DOI
, fulltext:postprint
).
Terms of use
These subroutines may be used freely without permission, but not
for commercial purposes. When used for research publications, we
kindly ask users to cite and acknowledge the source.
RBF-PUM-CD
Solve 2-D convection-diffusion problem in [0 1]x[0 1] with RBF-PUM
u_t = \kappa\Delta{u} + \nu\nabla{u}
with Dirichlet Boundary Conditions.
The PUM method is used with inverse multiquadric RBFs for the local interpolants
Involved functions
weight_PUM, imq_PUM, RBF_PUM_diffmat and ode_CD.
For the non-uniform discretization case based on Halton points,
uncomment the code line:
load hpoints.mat; xm=data(:,1); ym=data(:,2);
Download MATLAB files: RBF-PUM-CD.zip
RBF-PUM-BS (uniform-tailored)
Evaluate the two assets AMERICAN OPTION with RBF-PUM.
The RBF-PUM method is used with inverse multiquadric RBFs for the local interpolants.
The penalty parameters are \delta=0.00001, C=r.
Involved functions
weight_PUM, imq_PUM, BS_1D, PUM_BS_diffmat and odefun_2D.
PUM_BS_tailored.m is based on tailored nodes and
PUM_BS_uniform.m is based on uniform nodes.
Download MATLAB files: RBF-PUM-BS.zip
RBF-PUM-BS-GUI-callput
The two assets AMERICAN option calculator as a graphical user
interface (GUI).
solver_BS.m is the main program for implementation of the example.
Download MATLAB files: RBF-PUM-BS-GUI-callput.zip