Multistep collocation approximations to solutions of first-kind Volterra integral equations

被引：12

作者：

Zhang, Tingting ^{[1
]}

Liang, Hui ^{[1
,2
]}

机构：

[1] Heilongjiang Univ, Sch Math Sci, Harbin, Heilongjiang, Peoples R China

[2] Heilongjiang Prov Key Lab Theory & Computat Compl, Harbin, Heilongjiang, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2018年 / 130卷

关键词：

Volterra integral equations; First kind; Multistep collocation methods; Convergence; 1ST KIND; CONVERGENCE;

D O I：

10.1016/j.apnum.2018.04.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The multistep collocation method is applied to Volterra integral equations of the first kind. The existence and uniqueness of the multistep collocation solution are proved. Then the convergence condition of the multistep collocation method is analyzed and the corresponding convergence order is described. In particular, for c(m) = 1, the convergence conditions, which can be easily implemented, are given for two-step and three-step collocation methods. Numerical experiments illustrate the theoretical analysis. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：171 / 183

页数：13

共 13 条

[1]

Brunner, 2010, 7 LECTIRES THEORY NU

[2]

Brunner H., 1986, NUMERICAL SOLUTION V

[3] Multistep collocation methods for Volterra integro-differential equations [J].

Cardone, Angelamaria ;

Conte, Dajana .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 221 :770-785

[4] Multistep collocation methods for Volterra Integral Equations [J].

Conte, D. ;

Paternoster, B. .

APPLIED NUMERICAL MATHEMATICS, 2009, 59 (08) :1721-1736

[5] Two-step diagonally-implicit collocation based methods for Volterra Integral Equations [J].

Conte, Dajana ;

D'Ambrosio, Raffaele ;

Paternoster, Beatrice .

APPLIED NUMERICAL MATHEMATICS, 2012, 62 (10) :1312-1324

[6] Super implicit multistep collocation methods for nonlinear Volterra integral equations [J].

Fazeli, S. ;

Hojjati, G. ;

Shahmorad, S. .

MATHEMATICAL AND COMPUTER MODELLING, 2012, 55 (3-4) :590-607

[7] Numerical solution of Volterra integro-differential equations by superimplicit multistep collocation methods [J].

Fazeli, Somayyeh ;

Hojjati, Gholamreza .

NUMERICAL ALGORITHMS, 2015, 68 (04) :741-768

[8] Multistep Hermite collocation methods for solving Volterra Integral Equations [J].

Fazeli, Somayyeh ;

Hojjati, Gholamreza ;

Shahmorad, Sedaghat .

NUMERICAL ALGORITHMS, 2012, 60 (01) :27-50

[9]

Hairer E., SIAM J NUMER ANAL

[10] STABILITY AND CONVERGENCE OF MULTISTEP METHODS FOR LINEAR VOLTERRA INTEGRAL-EQUATIONS OF 1ST KIND [J].

HOLYHEAD, PAW ;

MCKEE, S .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1976, 13 (02) :269-292

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