Approximations to the solution of Cauchy problem for a linear evolution equation via the space shift operator (second-order equation example)

被引：6

作者：

Remizov, Ivan D. ^{[1
]}

机构：

[1] Natl Res Univ, Higher Sch Econ, 25-12 Bol Pecherskaya Ulitsa,Room 224, Nizhnii Novgorod 603155, Russia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 328卷

基金：

俄罗斯科学基金会;

关键词：

Cauchy problem; Linear parabolic PDE; Approximate solution; Shift operator; Chernoff theorem; Numerical method; QUASI-FEYNMAN FORMULAS; SCHRODINGER-EQUATION; PARABOLIC EQUATIONS; PATH-INTEGRALS; THEOREM;

D O I：

10.1016/j.amc.2018.01.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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. (c) 2018 Elsevier Inc. All rights reserved.

引用

页码：243 / 246

页数：4

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