Lagrangian Numerical Approximations to One-Dimensional Convolution-Diffusion Equations

@article{Gosse2006LagrangianNA,
  title={Lagrangian Numerical Approximations to One-Dimensional Convolution-Diffusion Equations},
  author={Laurent Gosse and Giuseppe Toscani},
  journal={SIAM J. Scientific Computing},
  year={2006},
  volume={28},
  pages={1203-1227}
}
This work focuses on the numerical analysis of 1D nonlinear diffusion equations involving a convolution product. First, homogeneous friction equations are considered. Algorithms follow recent ideas on mass transportation methods and lead to simple schemes which can be proved to be stable, to decrease entropy and to converge toward the unique solution of the continuous problem. In particular, for the first time, homogeneous cooling states are displayed numerically. Further, we present results on… CONTINUE READING