International Journal of Applied and Computational Mathematics 

About: International Journal of Applied and Computational Mathematics is an academic journal published by Springer Nature. The journal publishes majorly in the area(s): Nonlinear system & Heat transfer. It has an ISSN identifier of 2349-5103. Over the lifetime, 1180 publications have been published receiving 7937 citations. The journal is also known as: Int. J. Appl. Comput. Math & Applied and computational mathematics.

Numerical Analysis of the Unsteady Natural Convection MHD Couette Nanofluid Flow in the Presence of Thermal Radiation Using Single and Two-Phase Nanofluid Models for Cu–Water Nanofluids

Abstract: The unsteady Couette nanofluid flow with heat transfer is investigated numerically for copper–water nanofluids under the combined effects of thermal radiation and a uniform transverse magnetic field with variable thermo-physical properties, in the case where the flow is established vertically between two parallel plates, so that one of them has an accelerated motion. The homogeneous single-phase model (i.e., Tiwari and Das’s nanofluid model) and the two-phase mixture model (i.e., Buongiorno’s nanofluid model) are utilized in this study together with Corcione’s model to further investigate and clarify the differences between those models and evaluate the validity of the single-phase model for studying the unsteady natural convection MHD Couette nanofluid flow with thermal radiation. In this investigation, we assume that the studied nanofluid is electrically conducting and has a Newtonian rheological behavior. The nonlinear dynamical system of partial differential equations are solved numerically by means of the Gear–Chebyshev–Gauss–Lobatto collocation technique for zero nanoparticles mass flux and no-slip impermeable conditions at the isothermal vertical plates. In a special case, the present numerical solution is also validated analytically and numerically with the earlier available results. For both nanofluid models, the effects of major parameters on the dimensionless velocity, temperature and volumetric fraction of nanoparticles are analysed via representative profiles, whereas the skin friction factor and the heat transfer rate are estimated numerically and discussed through tabular illustrations.

Jacobi Elliptic Function Expansion Method for Solving KdV Equation with Conformable Derivative and Dual-Power Law Nonlinearity

Abstract: In this work, the KdV equation with conformable derivative and dual-power law nonlinearity is considered. It is exceedingly used as a model to depict the feeble nonlinear long waves in different fields of sciences. Furthermore, it explains the comparable effects of weak dispersion and weak nonlinearity on the evolvement of the nonlinear waves. Using the Jacobi elliptic function expansion method, new exact solutions of that equation have been found. As results, some obtained solutions behave as periodic traveling waves, bright soliton, and dark soliton.

Amplitude-Frequency Relationship for Conservative Nonlinear Oscillators with Odd Nonlinearities

Abstract: This paper studies a conservative nonlinear oscillator with odd nonlinearities, u $$^{\prime \prime }+f(u)=0$$ , the square of its frequency is f $$^{\prime }(\hbox {u}_\mathrm{i})$$ , where $$\hbox {u}_\mathrm{i}$$ is a location point. A criterion on how to choose a location point is given. Dufffing equation is used as an example to show the accuracy of the prediction.

Numerical Simulation of Entropy Generation on MHD Nanofluid Towards a Stagnation Point Flow Over a Stretching Surface

Abstract: In this article, entropy generation on MHD nanofluid towards a stagnation point flow over a permeable stretching surface has been investigated numerically. The governing equations of nanofluid are simplified using similarity variables with the help of momentum, energy and concentration equations. The resulting highly nonlinear coupled differential equations are solved with the help of successive linearization method and Chebyshev spectral collocation method. The impact of all the pertinent parameters such as Hartmann number, suction/injection parameter, heat source/sink parameter, Lewis number, Prandtl number, Brownian motion parameter, thermophoresis parameter are demonstrated graphically. Furthermore, the effect of Brinkman number and Reynolds number are also presented for entropy generation. It is analyzed that the velocity of the fluid increases due to greater influence of magnetic field and porosity parameter. Moreover, it is also observed that the entropy generation number increase due to the increment in Brinkman number and Reynolds number. Numerical comparison is also given with the existing published literature and found that the present results are in good agreement.

Study of the Analytical Treatment of the (2+1)-Dimensional Zoomeron, the Duffing and the SRLW Equations via a New Analytical Approach

Abstract: In this paper, we applied the improved tan (�(ξ )/ 2)-expansion scheme for the (2+1)-dimensional Zoomeron, the Duffing and the symmetric regularized long wave equa- tionsandexactparticularsolutionshavebeenfound.Theexactparticularsolutionscontaining four types hyperbolic function solution, trigonometric function solution, exponential solu- tion and rational solution. We obtained the further solutions comparing with other methods as sine-cosine function method (Qawasmeh in J Math Comput Sci 3:1475-1480, 2013). Recently this method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that this method, with the help of symbolic com- putation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.