DOI: https://doi.org/10.26089/NumMet.v24r213

On the hybrid projection method to a stable manifold of a one-dimensional Burgers-type equation

Authors

  • Anastasia B. Kalinina
  • Andrey A. Kornev
  • Vladimir S. Nazarov

Keywords:

Burgers type equation
a stable manifold
numerical methods

Abstract

The paper considers a Burgers type equation with polynomial nonlinearity and zero boundary conditions. For the range of parameters of interest, the identically zero solution of the problem is locally unstable, and in its neighborhood there exists a stable manifold having finite codimension. For the approximate construction of this manifold a combined iterative algorithm the initial data for which is constructed by an analytical method and has quadratic accuracy is proposed. It is numerically shown how significant this modification is allows to reduce the computational complexity of projection on the desired manifold for typical parameter values compared to the standard linear approximation. The results obtained allow generalization to multidimensional dissipative equations of a wide class and can be used to solve problems of asymptotic stabilization based on initial data, boundary conditions and a right-hand side.

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Published

2023-04-15

Issue

Vol. 24 (2023): Issue 2.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Anastasia B. Kalinina

School No. 2007,
• Methodologist

Andrey A. Kornev

Lomonosov Moscow State University,
Faculty of Mechanics and Mathematics
• Deputy Head of the Department;
Marchuk Institute of Numerical Mathematics of RAS (INM RAS)
• Leading Researcher

Vladimir S. Nazarov

Lomonosov Moscow State University,
Faculty of Mechanics and Mathematics
• PhD Student

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