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PSEM Approximations for Both Branches of Lambert Function with Applications

Author

Listed:
  • H. Vazquez-Leal
  • M. A. Sandoval-Hernandez
  • J. L. Garcia-Gervacio
  • A. L. Herrera-May
  • U. A. Filobello-Nino

Abstract

Transcendental functions are a fundamental building block of science and engineering. Among them, a relatively new function denominated as Lambert is highlighted. The importance of such function relies on the fact that it can perform novel isolation of variables. In this work, we propose two accurate piece-wise approximate solutions, one for the lower branch and another one for the upper branch, respectively. The proposed analytic approximations are obtained by using the power series extender method (PSEM) in combination with asymptotic solutions. In addition, we will compare some published approximations with our proposal, highlighting our advantages in terms of significant digits and speed of evaluation. Furthermore, the approximations are validated by the successful simulation of a problem of economy and other acoustic waves of nonlinear ions.

Suggested Citation

  • H. Vazquez-Leal & M. A. Sandoval-Hernandez & J. L. Garcia-Gervacio & A. L. Herrera-May & U. A. Filobello-Nino, 2019. "PSEM Approximations for Both Branches of Lambert Function with Applications," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-15, March.
    • Handle: RePEc:hin:jnddns:8267951
    DOI: 10.1155/2019/8267951
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    Cited by:

    1. Dejan Brkić & Pavel Praks, 2019. "Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function: Reply to Discussion," Mathematics, MDPI, vol. 7(5), pages 1-7, May.
    2. Lóczi, Lajos, 2022. "Guaranteed- and high-precision evaluation of the Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    3. Jamilla, Cristeta & Mendoza, Renier & Mező, István, 2020. "Solutions of neutral delay differential equations using a generalized Lambert W function," Applied Mathematics and Computation, Elsevier, vol. 382(C).

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