One-parameter imbedding techniques for the solution of nonlinear boundary-value problems

摘要

A powerful numerical tool for the solution of nonlinear boundary-value problems —the one-parameter imbedding technique—is suggested. The basic principle is more than twenty years old; however, its numerical utilization has had only a few restricted applications up until recent times. The methods are divided into two categories: one- and multi-loop techniques. It is shown that the multi-loop techniques are of correct and incorrect type. Based on correct procedures new iteration techniques may be developed. Numerical solutions of differential equations arising for the one-parameter imbedding methods are presented along with the corresponding iteration techniques. Some typical imbedding procedures are discussed, and practical application of the method is demonstrated on calculated examples.