Open AccessCollocation solutions for the time fractional telegraph equation using cubic B-spline finite elements
Author(s) -
Orkun Taşbozan,
Alaattin Esen
Publication year - 2019
Publication title -
analele universităţii din timişoara. seria matematică-informatică/analele universităţii de vest din timişoara. seria matematică-informatică
Language(s) - English
Resource type - Journals
eISSN - 1841-3307
pISSN - 1841-3293
DOI - 10.2478/awutm-2019-0020
Subject(s) - mathematics , discretization , collocation method , b spline , fractional calculus , mathematical analysis , nonlinear system , collocation (remote sensing) , numerical analysis , partial differential equation , telegrapher's equations , orthogonal collocation , differential equation , ordinary differential equation , computer science , physics , telecommunications , transmission line , quantum mechanics , machine learning
In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The L 1and L 2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms L 2 and L ∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs).