Browsing by Author "Johnston, S. J."

Now showing 1 - 5 of 5

A new algorithm for solving dynamic equations on a time scale
(2017) Baleanu, Dumitru; Haghbin, A.; Johnston, S. J.; Baleanu, Dumitru; 56389; Matematik
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.
Citation - WoS: 5
Citation - Scopus: 9
Complex B-Spline Collocation Method for Solving Weakly Singular Volterra Integral Equations of the Second Kind
(Univ Miskolc inst Math, 2015) Ramezani, M.; Jafari, H.; Johnston, S. J.; Baleanu, D.
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.
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; Matematik
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.
Citation - WoS: 43
Citation - Scopus: 46
Laplace homotopy perturbation method for Burgers equation with space- and time-fractional order
(Sciendo, 2016) Johnston, S. J.; Baleanu, Dumitru; Jafari, H.; Moshokoa, S. P.; Ariyan, V. M.; Baleanu, D.; 56389; Matematik
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.
Citation - WoS: 7
Citation - Scopus: 8
Stability of dirac equation in four-dimensional gravity
(Iop Publishing Ltd, 2017) Safari, F.; Baleanu, Dumitru; Jafari, H.; Sadeghi, J.; Johnston, S. J.; Baleanu, D.; 56389; Matematik
We introduce the Dirac equation in four-dimensional gravity which is a generally covariant form. We choose the suitable variable and solve the corresponding equation. To solve such equation and to obtain the corresponding bispinor, we employ the factorization method which introduces the associated Laguerre polynomial. The associated Laguerre polynomials help us to write the Dirac equation of four-dimensional gravity in the form of the shape invariance equation. Thus we write the shape invariance condition with respect to the secondary quantum number. Finally, we obtain the spinor wave function and achieve the corresponding stability of condition for the four-dimensional gravity system.