Browsing by Author "Johnston, S. J."

Now showing 1 - 4 of 4

A Decomposition Method for Solving Q-Difference Equations
(Natural Sciences Publishing Corporation, 2015) Baleanu, Dumitru; Jafari, H.; Johnston, S. J.; Sani, S. M.; 56389
The q-difference equations are important in q-calculus. In this paper, we apply the iterative method which is suggested by Daftardar and Jafari, hereafter called the Daftardar-Jafari method, for solving a type of q-partial differential equations. We discuss the convergency of this method. In the implementation of this technique according to other iterative methods such as Adomian decomposition and homotopy perturbation methods, one does not need the calculation of the Adomian's polynomials for nonlinear terms. It is proven that under a special constraint, the given result by this method converges to exact solution of nonlinear q-ordinary or q-partial differential equations. © 2015 NSP Natural Sciences Publishing Cor.
A new algorithm for solving dynamic equations on a time scale
(2017) Baleanu, Dumitru; Haghbin, A.; Johnston, S. J.; Baleanu, Dumitru; 56389
In this paper, we propose a numerical algorithm to solve a class of dynamic time scale equation which is called the q-difference equation. First, we apply the method for solving initial value problems (IVPs) which contain the first and second order delta derivatives. Illustrative examples show the usefulness of the method. Then we present applications of the method for solving the strongly non-linear damped q-difference equation. The results show that our method is more accurate than the other existing method. (C) 2016 Elsevier B.V. All rights reserved.
Complex b-spline collocation method for solving weaklysingular volterra integral equations of the second kind
(Univ Miskolc Inst Math, 2015) Baleanu, Dumitru; Ramezani, M.; Johnston, S. J.; Baleanu, Dumitru; 56389
In this paper we propose a new collocation type method for solving Volterra integral equations of the second kind with weakly singular kernels. In this method we use the complex B-spline basics in collocation method for solving Volterra integral. We compare the results obtained by this method with exact solution. A few numerical examples are presented to demonstrate the effectiveness of the proposed method.
Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order
(De Gruyter Open LTD, 2016) Baleanu, Dumitru; Jafari, Hossein; Moshokoa, S. P.; Ariyan, Vernon; Baleanu, Dumitru; 56389
The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.