108327 20240319080945.0 doi 10.1016/j.cam.2020.113267 sideral 121227 ART-2022-121227 eng Chand, A.K.B. Cubic spline fractal solutions of two-point boundary value problems with a non-homogeneous nowhere differentiable term 2022 Access copy available to the general public Unrestricted Fractal interpolation functions (FIFs) supplement and subsume all classical interpolants. The major advantage by the use of fractal functions is that they can capture either the irregularity or the smoothness associated with a function. This work proposes the use of cubic spline FIFs through moments for the solutions of a two-point boundary value problem (BVP) involving a complicated non-smooth function in the non-homogeneous second order differential equation. In particular, we have taken a second order linear BVP: y''(x)+Q(x)y'(x)+P(x)y(x)=R(x) with the Dirichlet''s boundary conditions, where P(x) and Q(x) are smooth, but R(x) may be a continuous nowhere differentiable function. Using the discretized version of the differential equation, the moments are computed through a tridiagonal system obtained from the continuity conditions at the internal grids and endpoint conditions by the derivative function. These moments are then used to construct the cubic fractal spline solution of the BVP, where the non-smooth nature of y'' can be captured by fractal methodology. When the scaling factors associated with the fractal spline are taken as zero, the fractal solution reduces to the classical cubic spline solution of the BVP. We prove that the proposed method is convergent based on its truncation error analysis at grid points. Numerical examples are given to support the advantage of the fractal methodology. info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 2.4 2022 MATHEMATICS, APPLIED 45 / 267 = 0.169 2022 Q1 T1 0.797 2022 Computational Mathematics 2022 Q2 Applied Mathematics 2022 Q2 5.4 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Tyada, K.R. Navascués, M.A. Universidad de Zaragoza (orcid)0000-0003-4847-0493 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 404 (2022), 113267 J. comput. appl. math. Journal of Computational and Applied Mathematics 0377-0427 520020 http://zaguan.unizar.es/record/108327/files/texto_completo.pdf Postprint 2188047 http://zaguan.unizar.es/record/108327/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:108327 articulos driver 2024-03-18-12:32:18 ARTICLE