The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation
Abstract
In this paper, we approximate the fractional derivative of a given function using the univariate multinode Shepard method through the Gauss-Jacobi quadrature formula. Subsequently, the proposed method is applied to the numerical solution of boundary value problems (BVPs) and initial value problems (IVPs), specifically addressing the Bagley-Torvik equations. Experimental results confirm the method's effectiveness, particularly in accurately approximating the Bagley-Torvik equation for both BVPs and IVPs.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.