Open AccessTruncation and convergence dynamics: KdV Burgers model in the sense of Caputo derivative
Author(s) -
Asıf Yokuş
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.47472
Subject(s) - mathematics , korteweg–de vries equation , von neumann stability analysis , burgers' equation , truncation error , convergence (economics) , fractional calculus , stability (learning theory) , truncation (statistics) , mathematical analysis , partial differential equation , numerical analysis , numerical stability , nonlinear system , computer science , physics , quantum mechanics , machine learning , economics , economic growth , statistics
This study examines the time fractional KdV Burgers equation with the initial conditions by using the extended result on Caputo formula, finite difference method (FDM). For this reason, various fractional differential operators are defined and analyzed. In order to check the stability of the numerical scheme, the Fourier-von Neumann technique is used. By presenting an example of KdV Burgers equation above mentioned issues are discussed and numerical solutions of the error estimates have been found for the FDM. For the errors in $L_2$ and $L_\infty$ the method accuracy has been controlled. Moreover, the obtained results have been compared with the exact solution for different cases of non-integer order and the behavior of the potentials u is presented as a graph. The numerical results have been shown in tables.