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

[31] Modified cauchy problem for a loaded second-order parabolic equation with constant coefficients
M. O. Mamchuev
Differential Equations, 2015, 51 : 1137 - 1144
[32] CAUCHY PROBLEM FOR A SECOND-ORDER EQUATION WITH 2 INDEPENDENT VARIABLES IN COMPLEX REGION
KRYLOV, AL
DOKLADY AKADEMII NAUK SSSR, 1968, 183 (04): : 765 - &
[33] Modified cauchy problem for a loaded second-order parabolic equation with constant coefficients
Mamchuev, M. O.
DIFFERENTIAL EQUATIONS, 2015, 51 (09) : 1137 - 1144
[34] Solution of Cauchy Problem for Equation First Order Via Haar Functions
Lukomskii, D. S.
Lukomskii, S. F.
Terekhin, P. A.
IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2016, 16 (02): : 151 - 159
[35] On the second order cauchy problem associated with a linear operator
1600, (154):
[36] On a family of solutions of a linear second-order differential equation with constant unbounded operator coefficients in a Banach space
V. I. Fomin
Differential Equations, 2008, 44 : 449 - 451
[37] On a family of solutions of a linear second-order differential equation with constant unbounded operator coefficients in a Banach space
Fomin, V. I.
DIFFERENTIAL EQUATIONS, 2008, 44 (03) : 449 - 451
[38] On the Boyarsky–Meyers Estimate for the Solution of the Dirichlet Problem for a Second-Order Linear Elliptic Equation with Drift
Yu. A. Alkhutov
G. A. Chechkin
Journal of Mathematical Sciences, 2024, 286 (1) : 1 - 13
[39] ASYMPTOTIC APPROXIMATIONS TO SOLUTIONS OF A SECOND-ORDER DIFFERENTIAL EQUATION
PITTS, CGC
QUARTERLY JOURNAL OF MATHEMATICS, 1966, 17 (68): : 307 - &
[40] Existence of a unique bounded solution to a linear second-order difference equation and the linear first-order difference equation
Stevo Stević
Advances in Difference Equations, 2017

← 1 2 3 4 5 →