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A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

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  • Mustafa Inc
  • Ali Akgül
  • Adem Kiliçman

Abstract

We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.

Suggested Citation

  • Mustafa Inc & Ali Akgül & Adem Kiliçman, 2013. "A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:578942
    DOI: 10.1155/2013/578942
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    References listed on IDEAS

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    1. Inc, Mustafa, 2007. "Numerical simulation of KdV and mKdV equations with initial conditions by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1075-1081.
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    Cited by:

    1. Mustafa Inc & Ali Akgül & Adem Kılıçman, 2013. "A New Application of the Reproducing Kernel Hilbert Space Method to Solve MHD Jeffery‐Hamel Flows Problem in Nonparallel Walls," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yu-Lan Wang & Hao Yu & Fu-Gui Tan & Shanshan Qu, 2014. "Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Ali Akgül & Adem Kiliçman, 2015. "Solving Delay Differential Equations by an Accurate Method with Interpolation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    4. F. Z. Geng & S. P. Qian, 2014. "Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. X. Y. Li & B. Y. Wu & R. T. Wang, 2014. "Reproducing Kernel Method for Fractional Riccati Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Mustafa Inc & Ali Akgül, 2014. "Numerical Solution of Seventh‐Order Boundary Value Problems by a Novel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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