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Robust numerical method for singularly perturbed semilinear parabolic differential difference equations

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  • Kabeto, Masho Jima
  • Duressa, Gemechis File

Abstract

This paper deals with the robust numerical method for solving the singularly perturbed semilinear partial differential equation with the spatial delay. The quadratically convergent quasilinearization technique is used to linearize the semilinear term. It is formulated by discretization of the solution domain and then replacing the differential equation by finite difference approximation that in turn gives the system of algebraic equations. The method is shown to be first-order convergent. It is observed that the convergence is independent of the perturbation parameter. Numerical illustrations are investigated on model examples to support the theoretical results and the effectiveness of the method.

Suggested Citation

  • Kabeto, Masho Jima & Duressa, Gemechis File, 2021. "Robust numerical method for singularly perturbed semilinear parabolic differential difference equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 537-547.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:537-547
    DOI: 10.1016/j.matcom.2021.05.005
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    Cited by:

    1. Hu, Chaoming & Wan, Zhao Man & Zhu, Saihua & Wan, Zhong, 2022. "An integrated stochastic model and algorithm for constrained multi-item newsvendor problems by two-stage decision-making approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 280-300.
    2. Justin B. Munyakazi & Olawale O. Kehinde, 2022. "A New Parameter-Uniform Discretization of Semilinear Singularly Perturbed Problems," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    3. Priyadarshana, S. & Mohapatra, J. & Pattanaik, S.R., 2023. "An improved time accurate numerical estimation for singularly perturbed semilinear parabolic differential equations with small space shifts and a large time lag," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 183-203.
    4. Kumar, Sunil & Sumit, & Vigo-Aguiar, Jesus, 2022. "A high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 287-306.

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