Cubic spline collocation for Volterra integral equations

被引：15

作者：

Oja, P ^{[1
]}

Saveljeva, D ^{[1
]}

机构：

[1] Univ Tartu, Inst Appl Math, EE-50409 Tartu, Estonia

来源：

COMPUTING | 2002年 / 69卷 / 04期

关键词：

cubic spline collocation; spline projections; Volterra integral equations; stability and convergence of spline collocation method;

D O I：

10.1007/s00607-002-1463-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In the standard step-by-step cubic spline collocation method for Volterra integral equations an initial condition is replaced by a not-a-knot boundary condition at the other end of the interval. Such a method is stable in the same region of collocation parameter as in the step-by-step implementation with linear splines. The results about stability and convergence are based on the uniform boundedness of corresponding cubic spline interpolation projections. The numerical tests given at the end completely support the theoretical analysis.

引用

页码：319 / 337

页数：19

共 14 条

[1]

Atkinson KE., 1996, NUMERICAL SOLUTION I

[2]

BAKER C, 1977, NUMERICAL TREATMENT

[3] The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations [J].

Brunner, H ;

Pedas, A ;

Vainikko, G .

MATHEMATICS OF COMPUTATION, 1999, 68 (227) :1079-1095

[4]

Brunner H., 1986, The Numerical Solution of Volterra Equations

[5]

El Tom M. E. A., 1974, BIT (Nordisk Tidskrift for Informationsbehandling), V14, P136, DOI 10.1007/BF01932942

[6]

Gelfond A. O., 1971, CALCULUS FINITE DIFF

[7]

Hackbusch W., 1995, INTEGRAL EQUATIONS T

[8]

HUNG HS, 1970, 1053 MRC U WISC

[9]

Krasnoselski MA., 1972, Approximate solution of operator equations

[10]

Oja P, 2001, INNOV APPL MATH, P405

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