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    Non-polynomial Cubic Spline Method for Three-Dimensional Wave Equation
    (Springer, 2023) Sattar, Rabia; Ahmad, Muhammad Ozair; Pervaiz, Anjum; Ahmed, Nauman; Akgül, Ali
    The scientific community has always been showing deep concern towards partial differential equations (PDEs) and to approximate its numerical solution. This research proposes a non-polynomial cubic spline-based numerical technique for approximating the three-dimensional (3D) wave equation with Dirichlet boundary conditions. The proposed method develops an algebraic scheme for 3D wave equation which can be solved for different spatial and temporal levels. The suggested method provides a three-time level scheme with higher accuracy of order O(h8+ k8+ ?8+ ?2h2+ ?2k2+ ?2?2) by electing appropriate parameter values involved in the spline function. The stability analysis of the suggested numerical technique has been examined and numerical solution of some selected problems are included to exhibit the validity of the proposed method. Numerical results of the test problems are prepared through tables and graphs to demonstrate the effectiveness of the presented work. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    Öğe
    NON-POLYNOMIAL CUBIC SPLINE METHOD USED TO FATHOM SINE GORDON EQUATIONS IN 3+1 DIMENSIONS
    (Vinca Inst Nuclear Sci, 2023) Sattar, Rabia; Ahmad, Muhammad Ozair; Pervaiz, Anjum; Ahmed, Nauman; Akgul, Ali; Abdullaev, Sherzod; Alshaikh, Noorhan
    This study contains an algorithmic solution of the Sine Gordon equation in three space and time dimensional problems. For discretization, the central difference formula is used for the time variable. In contrast, space variable x, y, and z are discretized using the non-polynominal cubic spline functions for each. The proposed scheme brings the accuracy of order O(h(2) + k(2) + sigma(2) + iota(2)h(2) + iota(2)k(2) + iota(2)sigma(2)) by electing suitable parametric values. The paper also discussed the truncation error of the proposed method and obtained the stability analysis. Numerical problems are elucidated by this method and compared to results taken from the literature.