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On the Numerical Simulation of HPDEs Using θ -Weighted Scheme and the Galerkin Method

Author

Listed:
  • Haifa Bin Jebreen

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11 551, Saudi Arabia
    These authors contributed equally to this work.)

  • Fairouz Tchier

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11 551, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ -weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Suggested Citation

  • Haifa Bin Jebreen & Fairouz Tchier, 2020. "On the Numerical Simulation of HPDEs Using θ -Weighted Scheme and the Galerkin Method," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:78-:d:473124
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    References listed on IDEAS

    as
    1. Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    2. S. Hadi Seyedi & Behzad Nemati Saray & Ali Ramazani, 2019. "High-Accuracy Multiscale Simulation of Three-Dimensional Squeezing Carbon Nanotube-Based Flow inside a Rotating Stretching Channel," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-18, August.
    Full references (including those not matched with items on IDEAS)

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