Higher Order Approximations in the Heat Equation and the Truncated Moment Problem

Yong Jung Kim, Wei-Ming Ni
2009 SIAM Journal on Mathematical Analysis  
In this paper we use linear combinations of n heat kernels to approximate solutions of the heat equation. In certain cases we are able to show that our approxi- For instance, for positive solutions of the heat equation such approximations are achieved using the theory of truncated moment problems. For general solutions of the heat equation, although approximations of this order is not guaranteed, a lower order approximation (e.g. of the order O(t ( 1 2p − n+1 2 ) ) ) is possible. These
more » ... ble. These theoretical convergence orders are also observed numerically.
doi:10.1137/08071778x fatcat:3cggi3g6jnar5iqebzgl7zrd3y