000108327 001__ 108327
000108327 005__ 20240319080945.0
000108327 0247_ $$2doi$$a10.1016/j.cam.2020.113267
000108327 0248_ $$2sideral$$a121227
000108327 037__ $$aART-2022-121227
000108327 041__ $$aeng
000108327 100__ $$aChand, A.K.B.
000108327 245__ $$aCubic spline fractal solutions of two-point boundary value problems with a non-homogeneous nowhere differentiable term
000108327 260__ $$c2022
000108327 5060_ $$aAccess copy available to the general public$$fUnrestricted
000108327 5203_ $$aFractal 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.
000108327 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000108327 590__ $$a2.4$$b2022
000108327 591__ $$aMATHEMATICS, APPLIED$$b45 / 267 = 0.169$$c2022$$dQ1$$eT1
000108327 594__ $$a5.4$$b2022
000108327 592__ $$a0.797$$b2022
000108327 593__ $$aComputational Mathematics$$c2022$$dQ2
000108327 593__ $$aApplied Mathematics$$c2022$$dQ2
000108327 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000108327 700__ $$aTyada, K.R.
000108327 700__ $$0(orcid)0000-0003-4847-0493$$aNavascués, M.A.$$uUniversidad de Zaragoza
000108327 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000108327 773__ $$g404 (2022), 113267$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427
000108327 8564_ $$s520020$$uhttps://zaguan.unizar.es/record/108327/files/texto_completo.pdf$$yPostprint
000108327 8564_ $$s2188047$$uhttps://zaguan.unizar.es/record/108327/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000108327 909CO $$ooai:zaguan.unizar.es:108327$$particulos$$pdriver
000108327 951__ $$a2024-03-18-12:32:18
000108327 980__ $$aARTICLE