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An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Author

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  • Eman S. Alaidarous
  • Malik Zaka Ullah
  • Fayyaz Ahmad
  • A.S. Al-Fhaid

Abstract

In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

Suggested Citation

  • Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
    • Handle: RePEc:hin:jnljam:259371
    DOI: 10.1155/2013/259371
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    Cited by:

    1. Ramandeep Behl & Ioannis K. Argyros, 2020. "A New Higher-Order Iterative Scheme for the Solutions of Nonlinear Systems," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    2. Fayyaz Ahmad & Shafiq Ur Rehman & Malik Zaka Ullah & Hani Moaiteq Aljahdali & Shahid Ahmad & Ali Saleh Alshomrani & Juan A. Carrasco & Shamshad Ahmad & Sivanandam Sivasankaran, 2017. "Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs," Complexity, Hindawi, vol. 2017, pages 1-30, May.
    3. Vikash Kumar Sinha & Prashanth Maroju, 2023. "New Development of Variational Iteration Method Using Quasilinearization Method for Solving Nonlinear Problems," Mathematics, MDPI, vol. 11(4), pages 1-11, February.
    4. Mozafar Rostami & Taher Lotfi & Ali Brahmand, 2019. "A Fast Derivative-Free Iteration Scheme for Nonlinear Systems and Integral Equations," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    5. Ullah, Malik Zaka & Serra-Capizzano, S. & Ahmad, Fayyaz & Al-Aidarous, Eman S., 2015. "Higher order multi-step iterative method for computing the numerical solution of systems of nonlinear equations: Application to nonlinear PDEs and ODEs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 972-987.

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