RT journal article
T1 Generalised forms of fractional Euler and Runge-Kutta methods using non-uniform grid
A1 Kumar, Pushpendra
A1 Ertuk, V. S.
A1 Murillo Arcila, Marina
A1 Harley, C.
A2 Matemáticas
K1 Euler method
K1 Runge-Kutta scheme
K1 New generalised Caputo-type fractional derivative
K1 Generalised Taylor formula
K1 Numerical simulations
AB In this paper, we propose generalised forms of three well-known fractional numerical methodsnamed as Euler, Runge-Kutta 2-step, and Runge-Kutta 4-step, respectively. The newversions we provide of these methods are derived by using a technique of non-uniform gridwhich is slightly di erent to all the previous existing versions of these algorithms. A newgeneralised form of well-known Caputo-type fractional derivative is used to derive the results.All necessary analysis related to the stability, convergence, and error bounds arealso provided. The precision of all simulated results are justi ed by performing a bunch ofpractical works in which some important examples have been solved by implementing thecode in Mathematica software. Finally, we give a brief discussion on the simulated resultswhich shows that the generalised methods are fully novel, e ective, strong, and very easy toimplement.
YR 2023
FD 2023
LK http://hdl.handle.net/10498/35335
UL http://hdl.handle.net/10498/35335
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026