Bibliographic Details
| Title: |
ON A METHOD FOR SOLVING THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE GARDNER EQUATION. |
| Authors: |
Bezrodnykh, S. I.1 (AUTHOR) sbezrodnykh@mail.ru, Pikulin, S. V.1 (AUTHOR) spikulin@gmail.com |
| Source: |
Journal of Mathematical Sciences. May2026, Vol. 299 Issue 2, p121-136. 16p. |
| Subject Terms: |
*Nonlinear evolution equations, *Numerical analysis, *Solitons, *Time integration scheme, *Algorithms, *Initial value problems, *Nonlinear waves |
| Abstract: |
In this paper, we consider the efficient solution for an initial-boundary value problem for the Gardner equation: a spatially one-dimensional nonlinear evolution equation describing a broad class of dispersive autowave processes. We propose a numerical-analytical method based on a combination of explicit and implicit time discretization schemes for various terms of the differential operator. We develop a new efficient algorithm to solve a sequence of auxiliary linear problems, relying on analytical representations using an explicit form of the fundamental system of solutions. We consider an example of a numerical solution of the initial-boundary value problem for the Gardner equation and compare the result with a known exact solution of the solitary traveling wave type. [ABSTRACT FROM AUTHOR] |
| Database: |
Academic Search Index |