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

共 50 条

[21] The Cauchy Problem for One Second Order Partial Differential Equation with Carleman Shift
Maksimova, E. A.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2022, 43 (06) : 1366 - 1372
[22] Cauchy problem for second-order linear differential equations with variable operator coefficients
Silchenko, YT
MATHEMATICAL NOTES, 1996, 60 (1-2) : 114 - 117
[23] The Cauchy Problem for One Second Order Partial Differential Equation with Carleman Shift
E. A. Maksimova
Lobachevskii Journal of Mathematics, 2022, 43 : 1366 - 1372
[24] A Probabilistic Representation of Solution to the Cauchy Problem for Evolution Equation with Differential Operator of Order Greater Than 2
Platonova M.V.
Journal of Mathematical Sciences, 2018, 229 (6) : 744 - 755
[25] On the second-order Euler equation with bounded operator coefficients in a Banach space
Fomin, VI
DIFFERENTIAL EQUATIONS, 2006, 42 (04) : 512 - 518
[26] On the second-order Euler equation with bounded operator coefficients in a Banach space
V. I. Fomin
Differential Equations, 2006, 42 : 512 - 518
[27] On one method for the analysis of the Cauchy problem for a singularly perturbed inhomogeneous second-order linear differential equation
E. E. Bukzhalev
Computational Mathematics and Mathematical Physics, 2017, 57 : 1635 - 1649
[28] On one method for the analysis of the Cauchy problem for a singularly perturbed inhomogeneous second-order linear differential equation
Bukzhalev, E. E.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (10) : 1635 - 1649
[29] EVOLUTION OPERATOR SOLUTION OF CAUCHY-PROBLEM FOR HAMILTON-JACOBI EQUATION
TAMBURRO, MB
ISRAEL JOURNAL OF MATHEMATICS, 1977, 26 (3-4) : 232 - 264
[30] ON CAUCHY PROBLEM FOR AN ITERATED LINEAR DIFFERENTIAL OPERATOR EQUATION
OLEVSKII, MN
DOKLADY AKADEMII NAUK SSSR, 1963, 148 (05): : 1026 - &

← 1 2 3 4 5 →