Approximations to the solution of Cauchy problem for a linear evolution equation via the space shift operator (second-order equation example)
作者：
Highlights：
•
摘要
We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The method is based on the Chernoff approximation procedure applied to a specially constructed shift operator. It is proven that approximations converge uniformly to the exact solution.
论文关键词：Cauchy problem,Linear parabolic PDE,Approximate solution,Shift operator,Chernoff theorem,Numerical method
论文评审过程：Received 17 May 2016, Revised 23 December 2017, Accepted 24 January 2018, Available online 10 February 2018, Version of Record 10 February 2018.
论文官网地址：https://doi.org/10.1016/j.amc.2018.01.057
