TWO-POINT TAYLOR EXPANSIONS AND ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

被引：5

作者：

Lopez, Jose L. ^{[1
]}

Perez Sinusia, Ester ^{[2
]}

机构：

[1] Univ Publ Navarra, Dept Ingn Matemat & Informat, Pamplona 31006, Spain

[2] Univ Zaragoza, Dept Matemat Aplicada, Zaragoza 50018, Spain

来源：

MATHEMATICS OF COMPUTATION | 2010年 / 79卷 / 272期

关键词：

Second-order linear differential equations; boundary value problem; Frobenius method; two-point Taylor expansions; DIFFERENTIAL-EQUATIONS;

D O I：

10.1090/S0025-5718-10-02370-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider second-order linear differential equations phi(x)y '' + f(x)y' + g(x)y = h(x) in the interval (-1, 1) with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions. We consider phi(x), f(x), g(x) and h(x) analytic in a Cassini disk with foci at x = +/- 1 containing the interval (-1, 1). The two-point Taylor expansion of the solution y(x) at the extreme points +/- 1 is used to give a criterion for the existence and uniqueness of solution of the boundary value problem. This method is constructive and provides the two-point Taylor approximation of the solution(s) when it exists.

引用

页码：2103 / 2115

页数：13

共 8 条

[1]

[Anonymous], 1996, INT J MATH EDUC SCI, DOI DOI 10.1080/0020739960270606

[2] Taylor polynomial solutions of linear differential equations [J].

Kesan, C .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 142 (01) :155-165

[3]

KING AC, 1954, ANN MATH STUD, V337, P167

[4]

LAX PD, 2003, PARABOLIC EQUATIONS

[5] Two-point Taylor expansions of analytic functions [J].

López, JL ;

Temme, NM .

STUDIES IN APPLIED MATHEMATICS, 2002, 109 (04) :297-311

[6] Multi-point Taylor approximations in one-dimensional linear boundary value problems [J].

Lopez, Jose L. ;

Sinusia, Ester Perez ;

Temme, Nico M. .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 207 (02) :519-527

[7]

Olde Daalhuis AB, 1998, SIAM REV, V40, P463, DOI 10.1137/S0036144597315341

[8]

STAKGOLD I, 1988, GREENS FUNCTIONS BOU

← 1 →