The Adomian decomposition method for solving delay differential equation

Evans, David; Raslan, K. R.

doi:10.1080/00207160412331286815

Cited by 200 publications

(162 citation statements)

References 8 publications

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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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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 recent years, many techniques have been applied to a large class of problems. In particular, generalized pantograph equations are numerically solved by using the Adomian decomposition method [7], the Taylor method is utilized in [14], and the Bessel matrix method based on collocation points is applied in [19]. Hermite polynomials have been used to find the approximate solutions of pantograph equations [16].…”

Section: Introductionmentioning

confidence: 99%

A Taylor operation method for solutions of generalized pantograph type delay differential equations

Yüzbaşı¹,

Ismailov²

2018

Turk J Math

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In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is that the method does not require collocation points. By using the proposed method, the generalized pantograph equation problem is reduced to a system of linear algebraic equations. The solving of this system gives the coefficients of our solution. Numerical examples are given to demonstrate the accuracy of the technique and the numerical results show that the error of the present method is superior to that of other methods.The residual correction technique is used to improve the accuracy of the approximate solution and estimation of absolute error. The estimation aspect of the residual method is useful when the exact solution of the considered equation is unknown and this feature of the method is shown in numerical examples.

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“…Chanquing and Jianhua studied the Adomian decomposition method to solve the nonlinear fractional differential equations in [27]. In [7], the technique was applied on delay differential equations. A comparison was made between Adomian decomposition and tau methods in [4] for finding the solution of Volterra integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%

Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

Rani

Mishra

2018

Eur. J. Pure Appl. Math.

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Abstract. In this paper, we establish a modified Laplace transform Adomian decomposition method for solving nonlinear Volterra integral and integro-differential equations. This technique is different from the standard Laplace Adomian decomposition method because of the terms involved in Adomian polynomials. Here, we have used Newton Raphson formula in place of the term u i in Adomian polynomials. The proposed scheme is investigated with some illustrative examples and has given reliable results.

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The Adomian decomposition method for solving delay differential equation

Cited by 200 publications

References 8 publications

Numerical Approach for Solving Fractional Pantograph Equation

Numerical Approach for Solving Fractional Pantograph Equation

A Taylor operation method for solutions of generalized pantograph type delay differential equations

Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

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