Selfsimilar extrapolation of nonlinear problems from smallvariable to largevariable limit
Abstract
Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters, are often of main physical interest. A method is described for predicting the largevariable behavior of solutions to nonlinear problems from the knowledge of only their smallvariable expansions. The method is based on selfsimilar approximation theory resulting in selfsimilar factor approximants. The latter can well approximate a large class of functions, rational, irrational, and transcendental. The method is illustrated by several examples from statistical and condensed matter physics, where the selfsimilar predictions can be compared with the available largevariable behavior. It is shown that the method allows for finding the behavior of solutions at large variables when knowing just a few terms of smallvariable expansions. Numerical convergence of approximants is demonstrated.
 Publication:

International Journal of Modern Physics B
 Pub Date:
 August 2020
 DOI:
 10.1142/S0217979220502082
 arXiv:
 arXiv:2106.07280
 Bibcode:
 2020IJMPB..3450208Y
 Keywords:

 Nonlinear physical problems;
 asymptotic series;
 selfsimilar extrapolation;
 largevariable behavior;
 numerical convergence;
 02.30.Mv;
 02.60.x;
 Approximations and expansions;
 Numerical approximation and analysis;
 Mathematical Physics
 EPrint:
 14 pages