Fast and precise spectral method for solving pantograph type Volterra integro-differential equations

被引：54

作者：

Ezz-Eldien, S. S. ^{[1
]}

Doha, E. H. ^{[2
]}

机构：

[1] Assiut Univ, Dept Math, Fac Sci, New Valley Branch, El Kharja 72511, Egypt

[2] Cairo Univ, Dept Math, Fac Sci, Giza, Egypt

来源：

NUMERICAL ALGORITHMS | 2019年 / 81卷 / 01期

关键词：

Operational matrix; Chebyshev polynomials; Collocation method; Pantograph differential equations; Volterra integro-differential equations; STABILITY;

D O I：

10.1007/s11075-018-0535-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper focuses on studying a general form of pantograph type Volterra integro-differential equations (PVIDEs). We apply a new collocation spectral approach, based on shifted Chebyshev polynomials, for converting such PVIDEs into systems of algebraic equations. In addition, we apply the new spectral approach for systems of pantograph type Volterra integro-differential equations (SPVIDEs). We investigate the error analysis of the proposed numerical approach. Also, we present some comparisons with other spectral approaches for clarifying the superiority of the new spectral approach.

引用

页码：57 / 77

页数：21

共 51 条

[1] Spectral methods for pantograph-type differential and integral equations with multiple delays [J].

Ali, Ishtiaq ;

Brunner, Hermann ;

Tang, Tao .

FRONTIERS OF MATHEMATICS IN CHINA, 2009, 4 (01) :49-61

[2]

Amin A. Z., 2016, Comput. Math. Appl., V4, P1, DOI [10.1016/j.camwa.2016.04.011, DOI 10.1016/J.CAMWA.2016.04.011]

[3]

[Anonymous], 1997, Numerical Analysis, Brooks

[4] Asymptotic stability properties of Theta-methods for the pantograph equation [J].

Bellen, A ;

Guglielmi, N ;

Torelli, L .

APPLIED NUMERICAL MATHEMATICS, 1997, 24 (2-3) :279-293

[5] Numerical solution of delay integro-differential equations by using Taylor collocation method [J].

Bellour, Azzeddine ;

Bousselsal, Mahmoud .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (10) :1491-1506

[6] Numerical algorithm for the variable-order Caputo fractional functional differential equation [J].

Bhrawy, A. H. ;

Zaky, M. A. .

NONLINEAR DYNAMICS, 2016, 85 (03) :1815-1823

[7] A new Jacobi spectral collocation method for solving 1+1 fractional Schrodinger equations and fractional coupled Schrodinger systems [J].

Bhrawy, A. H. ;

Doha, E. H. ;

Ezz-Eldien, S. S. ;

Van Gorder, Robert A. .

EUROPEAN PHYSICAL JOURNAL PLUS, 2014, 129 (12)

[8]

BHRAWY AH, 1954, J MATH, V13, P2483, DOI DOI 10.1007/s00009-015-0635-y

[9] Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays [J].

Brunner, Hermann .

FRONTIERS OF MATHEMATICS IN CHINA, 2009, 4 (01) :3-22

[10]

BUHMANN MD, 1974, MATH COMPUT, V60, P575, DOI DOI 10.1090/S0025-5718-1993-1176707-2

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