Rapid convergence of the iterative technique for first order initial value problems

被引：21

作者：

Cabada, A

Nieto, JJ

机构：

[1] Depto. de Análise Matemat., Facultade de Matemáticas, Univ. de Santiago de Compostela

来源：

APPLIED MATHEMATICS AND COMPUTATION | 1997年 / 87卷 / 2-3期

关键词：

D O I：

10.1016/S0096-3003(96)00285-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the convergence of the approximate solutions of the first order problem u'(t) = f(t, u(t)); u(0) = u(0). We prove that if there exists partial derivative(k)f/partial derivative u(k), k greater than or equal to 1, and it is a continuous function, then it is possible to construct two sequences of approximate solutions converging to a solution with rate of convergence of order k. (C) Elsevier Science Inc., 1997.

引用

页码：217 / 226

页数：10

共 7 条

[1]

Agarwal R. P., 1993, Uniqueness and nonuniqueness criteria for ordinary differential equations

[2]

BELLMAN R, 1973, METHODS NONLINEAR AN, V2

[3]

Bellman R.E., 1965, Quasilinearization and Non-linear Boundary-value Problems

[4]

Ladde GS., 1985, MONOTONE ITERATIVE T

[5] EXISTENCE AND MONOTONE METHOD FOR PERIODIC-SOLUTIONS OF 1ST-ORDER DIFFERENTIAL-EQUATIONS [J].

LAKSHMIKANTHAM, V ;

LEELA, S .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1983, 91 (01) :237-243

[6]

LAKSHMIKANTHAM V, 1968, DIFFERENTIAL INTEGRA, V1

[7]

Lakshmikantham V., 1994, NONLINEAR WORLD, V1, P59

← 1 →