Comparison on Solving a Class of Nonlinear Systems of Partial Differential Equations and Multiple Solutions of Second Order Differential Equations

  • Ali Akgül
  • Esra Karatas Akgül
  • Yasir Khan
  • Dumitru Baleanu
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 23)


We apply the reproducing kernel Hilbert space method to a class of nonlinear systems of partial differential equations and to get multiple solutions of second order differential equations. We have reached meaningful results. These results have been depicted by figures. This method is a very impressive technique for solving nonlinear systems of partial differential equations and second order differential equations.


  1. 1.
    Abbasbandy, S., Azarnavid, B., Alhuthali, M.S.: A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems. J. Comput. Appl. Math. 279, 293–305 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Akgül, A.: A new method for approximate solutions of fractional order boundary value problems. Neural Parallel Sci. Comput. 22(1–2), 223–237 (2014)MathSciNetGoogle Scholar
  3. 3.
    Castro, L.P., Rodrigues, M.M., Saitoh, S.: A fundamental theorem on initial value problems by using the theory of reproducing kernels. Complex Anal. Oper. Theory 9(1), 87–98 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cui, M., Lin, Y.: Nonlinear Numerical Analysis in the Reproducing Kernel Space. Nova Science, New York (2009)zbMATHGoogle Scholar
  5. 5.
    Inc, M., Akgül, A., Geng, F.: Reproducing kernel Hilbert space method for solving Bratu’s problem. Bull. Malays. Math. Sci. Soc. 38, 271–287 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ketabchi, R., Mokhtari, R., Babolian, E.: Some error estimates for solving Volterra integral equations by using the reproducing kernel method. J. Comput. Appl. Math. 273, 245–250 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Mohammadi, M., Mokhtari, R.: A reproducing kernel method for solving a class of nonlinear systems of PDEs. Math. Model. Anal. 19(2), 180–198 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Zayed, A.I.: Solution of the energy concentration problem in reproducing-kernel Hilbert space. SIAM J. Appl. Math. 75(1), 21–37 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Ali Akgül
    • 1
  • Esra Karatas Akgül
    • 2
  • Yasir Khan
    • 3
  • Dumitru Baleanu
    • 4
  1. 1.Siirt UniversityArt and Science Faculty, Department of MathematicsSiirtTurkey
  2. 2.Siirt UniversityFaculty of Education, Department of MathematicsSiirtTurkey
  3. 3.University of Hafr Al-BatinDepartment of MathematicsHafr Al-BatinSaudi Arabia
  4. 4.Department of MathematicsÇankaya UniversityAnkaraTurkey

Personalised recommendations