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A new kernel functions based approach for solving 1-D interface problems

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  • Li, X.Y.
  • Wu, B.Y.

Abstract

In this work, a new numerical method is proposed for solving 1-D elliptic type interface problems. The methods is a combination of the multi-step reproducing kernel functions collocation techniques and the shooting method. Firstly the boundary value problems are converted to the initial value problem with interface conditions by the shooting method. Then multi-step reproducing kernel functions collocation techniques are proposed for solving the reduced linear initial value problems. Finally, some numerical example are presented to show the accuracy of this method.

Suggested Citation

  • Li, X.Y. & Wu, B.Y., 2020. "A new kernel functions based approach for solving 1-D interface problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302459
    DOI: 10.1016/j.amc.2020.125276
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    References listed on IDEAS

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    1. Wang, Yang & Chen, Yanping & Huang, Yunqing, 2020. "A two-grid method for semi-linear elliptic interface problems by partially penalized immersed finite element methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 1-15.
    2. Sahihi, Hussein & Abbasbandy, Saeid & Allahviranloo, Tofigh, 2019. "Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 583-598.
    3. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
    4. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    5. Ferreira, José Claudinei & Baquião, Maria Caruline, 2019. "A least square point of view to reproducing kernel methods to solve functional equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 206-221.
    6. Alvandi, Azizallah & Paripour, Mahmoud, 2019. "The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 151-160.
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