Hybrid journal (It can contain Open Access articles) ISSN (Print) 1752-2862 - ISSN (Online) 1752-2870 Published by Inderscience Publishers[447 journals]

Authors:Samad Parvin, Habib Shahbazi Shiran, Maryam Mastalizadeh Pages: 1 - 20 Abstract: In reaction-diffusion systems with non-standard diffusion, the memory of the transport process causes a coupling of reaction and diffusion. A generalisation of the Fick's law has been suggested to account for this coupling. Furthermore, the resultant effects of the interplay of transport, memory and reaction lend themselves to some interesting physics which is still not well understood because the governing equation as well as the accompanying memory integral and nonlinear reaction terms are not always amenable to tidy analytic or numerical expressions. Hence, the derivation of a suitable governing integro-differential equation as well as the approximate solution demands a considerable level of attention'. The main focus of this work can be seen as a contribution towards this objective. In this report, we develop and apply a hybrid boundary integral-finite element - finite difference numerical procedure to investigate an integro-differential-Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) - type kinetics. We also focus on scalar evolution for cases where the reaction coefficient takes on relatively large values. Although we are still far from a rigorous mathematical analysis, it has been found that the numerical results obtained compared favourably with existing benchmark solutions. This not only validates the current numerical formulation but also justifies the physics of the resulting front propagation. Keywords: hybrid numerical formulation; boundary integral; finite element; finite difference; Fisher-Klomogorov-Petrovskii-Piskunov equation; memory term; nonlinear; reaction-diffusion; integro-differential partial differential equation Citation: International Journal of Applied Nonlinear Science, Vol. 3, No. 1 (2018) pp. 1 - 20 PubDate: 2019-01-15T23:20:50-05:00 DOI: 10.1504/IJANS.2018.097323 Issue No:Vol. 3, No. 1 (2019)

Authors:Salahaldeen Rabba, Katrin Rohlf Pages: 21 - 40 Abstract: A second-order nonlinear differential equation is derived for the pressure of a compressible flow with slip at the wall through a constricted cylinder. The ideal gas equation of state is used, and the Karman-Pohlhausen method is utilised to derive the pressure differential equation from the Navier-Stokes equations of motion for a Newtonian viscous fluid. The solution for pressure is determined numerically and assessed in various flow geometries. This work is an extension of existing assessments in that nonlinear terms are kept in the differential equation for pressure, as well as second-order derivative terms. Additionally, wall slip and compressibility are incorporated in the equations, as well as geometries that are asymmetric with respect to the location of maximum constriction. Keywords: pressure; gradient; compressible; stenosis; Navier-Stokes; slip; Karman-Pohlhausen; asymmetric; nonlinear; constriction Citation: International Journal of Applied Nonlinear Science, Vol. 3, No. 1 (2018) pp. 21 - 40 PubDate: 2019-01-15T23:20:50-05:00 DOI: 10.1504/IJANS.2018.097324 Issue No:Vol. 3, No. 1 (2019)

Authors:Martin Hermann, Dieter Kaiser Pages: 41 - 65 Abstract: In the applications, the homotopy analysis method (HAM) is an often used method to determine an analytical approximate solution of lower-dimensional nonlinear ordinary differential equations. This approximation consists of an infinite series which depends on an auxiliary real parameter <i>h</i>. This parameter must be adjusted such that the series converges towards the exact solution of the given problem. In this paper we propose a computational approach, which is based on the residual of the truncated series, to determine an optimal value <i>h</i><SUB align="right">opt or an optimal region for <i>h</i>. Using the numerical computing environment MATLAB, we describe several possibilities how this approach can be realised. Finally, by means of three examples (an IVP, a two-point BVP, as well as a BVP on an infinite interval) we show how this mathematically sophisticated strategy can be applied and we present the optimal parameter <i>h</i><SUB align="right">opt for each example. Keywords: nonlinear ODE; homotopy analysis method; HAM; auxiliary parameter Citation: International Journal of Applied Nonlinear Science, Vol. 3, No. 1 (2018) pp. 41 - 65 PubDate: 2019-01-15T23:20:50-05:00 DOI: 10.1504/IJANS.2018.097325 Issue No:Vol. 3, No. 1 (2019)

Authors:Vishal Gupta, R.K. Saini, Raman Deep Pages: 66 - 76 Abstract: In this paper, we proved fixed point results for the functions satisfying <i>ϕ</i>-contraction and mixed g-monotone property. We also give an example in support of our result. Keywords: tripled fixed point; G-metric space; mixed g-monotone property Citation: International Journal of Applied Nonlinear Science, Vol. 3, No. 1 (2018) pp. 66 - 76 PubDate: 2019-01-15T23:20:50-05:00 DOI: 10.1504/IJANS.2018.097349 Issue No:Vol. 3, No. 1 (2019)