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

Approximations to the solution of Cauchy problem for a linear evolution equation via the space... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

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

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.057
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

References

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