Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, Tamil Nadu, India.
PLoS One. 2023 Dec 15;18(12):e0295525. doi: 10.1371/journal.pone.0295525. eCollection 2023.
Splines are piecewise polynomials that are as smooth as they can be without forming a single polynomial. They are linked at specific points known as knots. Splines are useful for a variety of problems in numerical analysis and applied mathematics because they are simple to store and manipulate on a computer. These include, for example, numerical quadrature, function approximation, data fitting, etc. In this study, cubic B-spline (CBS) functions are used to numerically solve the time fractional diffusion wave equation (TFDWE) with Caputo-Fabrizio derivative. To discretize the spatial and temporal derivatives, CBS with θ-weighted scheme and the finite difference approach are utilized, respectively. Convergence analysis and stability of the presented method are analyzed. Some examples are used to validate the suggested scheme, and they show that it is feasible and fairly accurate.
样条是分段多项式，它们在不形成单个多项式的情况下尽可能平滑。它们在称为节点的特定点处连接。样条在数值分析和应用数学的各种问题中都很有用，因为它们在计算机上存储和处理都很简单。这些问题包括数值求积、函数逼近、数据拟合等。在这项研究中，使用三次 B 样条（CBS）函数数值求解具有 Caputo-Fabrizio 导数的时间分数扩散波方程（TFDWE）。为了离散空间和时间导数，分别使用具有θ加权方案的 CBS 和有限差分方法。分析了所提出方法的收敛性和稳定性。使用一些例子验证了所提出的方案，结果表明它是可行的，并且相当准确。
