Chaplygin Method

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Chaplygin Method

 

a method of approximate integration of differential equations. Proposed by S. A. Chaplygin in 1919, the method permits an approximate solution to be found for a differential equation to a given degree of accuracy. It involves the construction of sequences of functions {un} and {vn} that approximate with continually increasing accuracy the desired solution y of a given differential equation and that fulfill the following relations:

unun + 1yvn+1vn

The construction of the sequences {un} and {vn} is based on Chaplygin’s theorem of differential inequalities and is a generalization of Newton’s method to the case of differential equations. The rate of convergence is the same as in Newton’s method; that is, uny tends to zero like

C/22n

REFERENCE

Chaplygin, S. A. Novyi metod priblizhennogo integrirovaniia differentsial’nykh uravnenii. Moscow-Leningrad, 1950.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.