%0 Journal Article 
%A Kumar, Pushpendra
%A Ertuk, V. S.
%A Murillo Arcila, Marina
%A Harley, C.
%T Generalised forms of fractional Euler and Runge-Kutta methods using non-uniform grid
%D 2023
%U http://hdl.handle.net/10498/35335
%X In this paper, we propose generalised forms of three well-known fractional numerical methods
named as Euler, Runge-Kutta 2-step, and Runge-Kutta 4-step, respectively. The new
versions we provide of these methods are derived by using a technique of non-uniform grid
which is slightly di erent to all the previous existing versions of these algorithms. A new
generalised 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 are
also provided. The precision of all simulated results are justi ed by performing a bunch of
practical works in which some important examples have been solved by implementing the
code in Mathematica software. Finally, we give a brief discussion on the simulated results
which shows that the generalised methods are fully novel, e ective, strong, and very easy to
implement.
%K Euler method
%K Runge-Kutta scheme
%K New generalised Caputo-type fractional derivative
%K Generalised Taylor formula
%K Numerical simulations
%~ Universidad de Cádiz