A novel method for nonlinear two-point boundary value problems: Combination of ADM and RKM

Geng, Fazhan; Cui, Minggen

doi:10.1016/j.amc.2010.11.020

Cited by 30 publications

(27 citation statements)

References 29 publications

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“…This example was solved in [28] using a combination of the ADM and the reproducing kernel method (RKM). In Table 4, MATHEMATICA is used to compare the absolute errors OEy(x) À S 5 (x)OE with those of Ref.…”

Section: Example 1 Consider the Following Linear Bvpmentioning

confidence: 99%

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Piece-wise continuous solution to a class of nonlinear boundary value problems

El‐Kalla

2013

Ain Shams Engineering Journal

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Section: Example 1 Consider the Following Linear Bvpmentioning

confidence: 99%

“…In Table 4, MATHEMATICA is used to compare the absolute errors OEy(x) À S 5 (x)OE with those of Ref. [28].…”

Section: Example 1 Consider the Following Linear Bvpmentioning

confidence: 99%

Piece-wise continuous solution to a class of nonlinear boundary value problems

El‐Kalla

2013

Ain Shams Engineering Journal

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“…However, for the solution of boundary value problems using ADM, it is necessary to determine some unknown parameters and therefore, it is required to solve nonlinear algebraic equations. Geng and Cui (2011) proposed a method for solving nonlinear second order two-point BVP by the combination of ADM and RKM. The fourth order three-point BVP described in this paper has been solved by extending the method developed by Geng and Cui (2011).…”

Section: Introductionmentioning

confidence: 99%

“…Geng and Cui (2011) proposed a method for solving nonlinear second order two-point BVP by the combination of ADM and RKM. The fourth order three-point BVP described in this paper has been solved by extending the method developed by Geng and Cui (2011).…”

Section: Introductionmentioning

confidence: 99%

Solution of fourth order three-point boundary value problem using ADM and RKM

Akram

Aslam

2016

Journal of the Association of Arab Universities for Basic and A

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In this paper, a computational method is proposed, for solving linear and nonlinear fourth order three-point boundary value problem (BVP) and the system of nonlinear BVP. This method is based on the Adomian decomposition method (ADM) and the reproducing kernel method (RKM). The solution of linear fourth order three-point boundary value problem (BVP) is determined by the reproducing kernel method, and the solution of nonlinear fourth order three-point BVP is determined using the combination of Adomian decomposition method and reproducing kernel method. The approximate solutions are given in the form of series. Numerical results are shown to illustrate the accuracy of the present method.ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

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“…Reproducing kernel theory has important application in numerical analysis, differential equations, probability, and statistics. Recently, using the RKM, some authors discussed telegraph equation [15], Troesch's porblem [16], MHD Jeffery-Hamel flow [17], Bratu's problem [18], KdV equation [19], fractional differential equation [20], nonlinear oscillator with discontinuity [21], nonlinear twopoint boundary value problems [22], integral equations [23], and nonlinear partial differential equations [24].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method

Inc

Akgül

Kılıçman

2013

Abstract and Applied Analysis

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We investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the form of a series in reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of this method. The results obtained from this method are compared with the exact solutions and other methods. Results of numerical examples show that this method is simple, effective, and easy to use.

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A novel method for nonlinear two-point boundary value problems: Combination of ADM and RKM

Cited by 30 publications

References 29 publications

Piece-wise continuous solution to a class of nonlinear boundary value problems

Piece-wise continuous solution to a class of nonlinear boundary value problems

Solution of fourth order three-point boundary value problem using ADM and RKM

Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method

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