Yazar "Ejaz, Syeda Tehmina" seçeneğine göre listele

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    A comprehensive study of subdivision collocation method for Burgers' equation
    (Taylor & Francis Inc, 2024) Ejaz, Syeda Tehmina; Bibi, Saima; Akgul, Ali; Hassani, Murad Khan
    This study explores the use of subdivision schemes to efficiently solve Burgers' equation. Burgers' equation is a fundamental fluid dynamics equation that describes the nonlinear behavior of fluid flow. This type of nonlinear equation is difficult to solve analytically, which makes the numerical solution an important tool. The subdivision collocation method (SCM) converts Burgers' equation into a system of algebraic linear equations using the quasilinearization technique. The results of this study demonstrate that the proposed approach yields accurate numerical solutions for Burgers' equation. Additionally, the subdivision approach is computationally efficient and requires fewer computational resources than existing numerical methods, making it a promising tool for solving Burgers' equation in practical applications. Overall, this study provides valuable insights into the approximate solution of Burgers' equation by implementing subdivision schemes.
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    Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study
    (Nature Portfolio, 2024) Malik, Safia; Ejaz, Syeda Tehmina; Akgul, Ali; Hassani, Murad Khan
    The current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. The proposed technique is examined on a variety of problems and the obtained results are presented both quantitatively in tables and visually in figures. Additionally, a comparative analysis is conducted between the numerical outcomes of the proposed technique with previously published methods to validate the correctness and accuracy of the current approach. The primary objective of this research is to investigate the application of subdivision schemes in the fields of physical sciences and engineering. Our approach involves transforming the problem into a set of algebraic equations.
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    Numerical Solutions of Volterra Integral Equations with Subdivision-Based Collocation Approach
    (World Scientific Publ Co Pte Ltd, 2024) Iqbal, Zainab; Ejaz, Syeda Tehmina; Akguel, Ali; Javaid, Ureen
    Integral equations play a vital role in the fields of applied and computational mathematics. This paper introduces a unique subdivision-based collocation technique for solving the initial value problems (IVPs) arising from Volterra integral equations (VIEs). A suitable subdivision scheme is employed to develop the numerical algorithm for solving the VIEs. Several numerical illustrations are tested and compared with the existing methods for assessing the efficiency of the proposed numerical algorithm and error estimation.
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    Subdivision collocation method for numerical treatment of regularized long wave (RLW) equation
    (Aip Publishing, 2024) Ejaz, Syeda Tehmina; Qamar, Syeda Asma; Akgul, Ali; Hassani, Murad Khan
    This research project introduces a novel computational approach for solving the regularized long wave equation. The proposed method utilizes a subdivision scheme with appropriate basis functions to transform the equation into a system of linear algebraic equations. A suitable numerical technique is employed to compute the solution of the transformed equations. Theoretical analysis of stability and error for the proposed method is also conducted. Furthermore, the invariants of three physical properties, waves, mass (M), momentum (P), and energy (e), are calculated. Additionally, numerical evidence is presented to demonstrate the effectiveness and accuracy of the method. The results of the numerical experiments confirm the efficiency and high accuracy of the proposed method. Moreover, the numerical results of the invariants validate the conservation laws and align with the theoretical results.