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Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives

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  • Abdon Atangana
  • Suares Clovis Oukouomi Noutchie

Abstract

We propose a powerful iteration scheme for solving analytically a class of partial equations with mixed derivatives. Our approach is based upon the Lagrange multiplier in two‐dimensional spaces. The local convergence and uniqueness of the proposed method are analyzed. In order to demonstrate the applicability of our method, we present an algorithm to compute the solution for two examples.

Suggested Citation

  • Abdon Atangana & Suares Clovis Oukouomi Noutchie, 2014. "Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:369304
    DOI: 10.1155/2014/369304
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    References listed on IDEAS

    as
    1. Abdon Atangana & Adem Kılıçman, 2013. "The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    2. Hector Vazquez-Leal & Arturo Sarmiento-Reyes & Yasir Khan & Uriel Filobello-Nino & Alejandro Diaz-Sanchez, 2012. "Rational Biparameter Homotopy Perturbation Method and Laplace‐Padé Coupled Version," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Hector Vazquez-Leal & Arturo Sarmiento-Reyes & Yasir Khan & Uriel Filobello-Nino & Alejandro Diaz-Sanchez, 2012. "Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, December.
    4. Abdon Atangana & Adem Kılıçman, 2013. "The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat‐Like Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Zdeněk Šmarda & Yasir Khan, 2012. "Singular Initial Value Problem for a System of Integro‐Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Zdeněk Šmarda & Yasir Khan, 2012. "Singular Initial Value Problem for a System of Integro-Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, December.
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