On the attainable order of collocation methods for pantograph integro-differential equations

Muroya, Yoshiaki; Ishiwata, Emiko; Brunner, Hermann

doi:10.1016/s0377-0427(02)00716-1

Cited by 60 publications

(36 citation statements)

References 10 publications

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“…Algorithm PIA (1,2). In PIA(1, 2) algorithm, we put forward a perturbation-iteration algorithm by taking one correction term in the perturbation expansion and correction terms of up to second derivatives in the Taylor expansion; that is, = 1, = 2.…”

Section: Perturbation-iterationmentioning

confidence: 99%

“…It arises in rather different fields of pure and applied mathematics, such as electrodynamics, control systems, number theory, probability, and quantum mechanics. Many researchers have studied the pantograph-type delay differential equation using analytical and numerical techniques [1][2][3][4][5][6][7][8]. The second-order pantograph-type delay differential equation is given as [7,8] …”

Section: Introductionmentioning

confidence: 99%

“…To the authors' knowledge, the application of perturbation-iteration algorithms to pantograph-type delay differential equations is novel. The two types of perturbation-iteration algorithms, PIA(1, 1) and PIA (1,2), are introduced in the next section. Then, the method is applied to pantograph equations via six examples, two of which are first-order linear, one is first-order nonlinear, and the others are second-order nonlinear; they showed excellent agreement with the published results and verified the accuracy and efficiency of the present method.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

Bahşı

Çevik

2015

Journal of Applied Mathematics

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The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases.

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Section: Perturbation-iterationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

Bahşı

Çevik

2015

Journal of Applied Mathematics

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“…Pantograph equation was studied by many authors and solved several numerical methods. The most important them are collocation method [4], spline method [5], Runga-Kutta method [6], Adomian decomposition method [7], homotopy perturbation method [8] etc. There are several pantograph equation kind in literature.…”

Section: Nowadays Notable Contributions Have Been Made Theory and Appmentioning

confidence: 99%

Numerical Approach for Solving Fractional Pantograph Equation

Anapali¹,

Öztürk²,

Gülsu³

2015

IJCA

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In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of linear algebraic equation using Maple 14 and we obtain the coefficients of Taylor expansion. In addition illustrative example is presented to demonstrate the effectiveness of the proposed method.

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“…which is a generalized of the pantograph equations given in [1][2][3]17], with the initial conditions …”

Section: Introductionmentioning

confidence: 99%

A taylor collocation method for solving high-order linear pantograph equations with linear functional argument

Gülsu

Sezer

2010

Numer. Methods Partial Differential Eq.

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On the attainable order of collocation methods for pantograph integro-differential equations

Cited by 60 publications

References 10 publications

Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

Numerical Approach for Solving Fractional Pantograph Equation

A taylor collocation method for solving high-order linear pantograph equations with linear functional argument

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