Applied and Computational Mathematics

Volume 11, Issue 2, April 2022

  • A Unified Singular Solution of Laplace’s Equation with Neumann and Dirichlet Boundary Conditions

    Jyh-Haw Tang, Chao-Kang Feng

    Issue: Volume 11, Issue 2, April 2022
    Pages: 38-47
    Received: Mar. 10, 2022
    Accepted: Apr. 02, 2022
    Published: Apr. 09, 2022
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    Abstract: Laplace’s equation is one of the important equations in studying applied mathematics and engineering problems including the study of temperature distribution of steady-state heat conduction or the concentration distribution of steady-state diffusion problems. In this study, the analytical method has been applied to solve the Laplace's equation in a... Show More
  • Homotopy Perturbation Method for Solving Nonlinear Fractional Reaction Diffusion Systems

    Khaled Abdalla Ishag, Mohamed Ahmed Abdallah, Abulfida Mohamed Ahmed

    Issue: Volume 11, Issue 2, April 2022
    Pages: 48-55
    Received: Mar. 22, 2022
    Accepted: Apr. 11, 2022
    Published: Apr. 20, 2022
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    Abstract: This study presents the Homotopy Perturbation Method (HPM) for nonlinear fractional reaction diffusion systems, the fractional derivatives are described in the caputo's' fractional operator. The study focus on three systems of fractional reaction diffusion equations in one, two and three dimensions, in this method, the solution considered as the su... Show More
  • A Simple Reform for Treating the Loss of Accuracy of Humlíček’s W4 Algorithm Near the Real Axis

    Mofreh Ramadan Zaghloul

    Issue: Volume 11, Issue 2, April 2022
    Pages: 56-59
    Received: Mar. 20, 2022
    Accepted: Apr. 06, 2022
    Published: Apr. 25, 2022
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    Abstract: Rapid evaluation of the Faddeyeva function, also known as the complex probability function, is essential to many spectroscopic and stellar applications. Humlíček’s W4 Algorithm is widely used in the literature for rapid and marginally accurate evaluation of the function (~10-4). However, as reported in the literature, the algorithm lose its claimed... Show More