A comparison of analytical solutions of nonlinear complex generalized Zakharov dynamical system for various definitions of the differential operator

<abstract><p>This paper considers deriving new exact solutions of a nonlinear complex generalized Zakharov dynamical system for two different definitions of derivative operators called conformable and $ M- $ truncated. The system models the spread of the Langmuir waves in ionized plasma. The extended rational $ sine-cosine $ and $ sinh-cosh $ methods are used to solve the considered system. The paper also includes a comparison between the solutions of the models containing separately conformable and $ M- $ truncated derivatives. The solutions are compared in the $ 2D $ and $ 3D $ graphics. All computations and representations of the solutions are fulfilled with the help of Mathematica 12. The methods are efficient and easily computable, so they can be applied to get exact solutions of non-linear PDEs (or PDE systems) with the different types of derivatives.</p></abstract>

Analysis of thermally stratified radiative flow of Sutterby fluid with mixed convection

In this attempt, we investigate the mixed convection in Sutterby fluid flow based on boundary layer approximation. Heat transport analysis is composed of stratification and thermal radiative phenomena. The system of non-linear PDEs is transformed into coupled ODEs. Convergent series approximations are evaluated via homotopic technique. Influence of various pertinent parameters is sketched and graphically analyzed. It is found that horizontal velocity increments for higher mixed convection parameter. The radiation parameter has a similar relation with temperature whereas the stratification parameter shows opposite behavior for temperature field.

Crossbreed impact of double-diffusivity convection on peristaltic pumping of magneto Sisko nanofluids in non-uniform inclined channel: A bio-nanoengineering model

The consequences of double-diffusivity convection on the peristaltic transport of Sisko nanofluids in the non-uniform inclined channel and induced magnetic field are discussed in this article. The mathematical modeling of Sisko nanofluids with induced magnetic field and double-diffusivity convection is given. To simplify PDEs that are highly nonlinear in nature, the low but finite Reynolds number, and long wavelength estimation are used. The Numerical solution is calculated for the non-linear PDEs. The exact solution of concentration, temperature and nanoparticle are obtained. The effect of various physical parameters of flow quantities is shown in numerical and graphical data. The outcomes show that as the thermophoresis and Dufour parameters are raised, the profiles of temperature, concentration, and nanoparticle fraction all significantly increase.

Increased space-parallelism via time-simultaneous Newton-multigrid methods for nonstationary nonlinear PDE problems

We discuss how “parallel-in-space & simultaneous-in-time” Newton-multigrid approaches can be designed which improve the scaling behavior of the spatial parallelism by reducing the latency costs. The idea is to solve many time steps at once and therefore solving fewer but larger systems. These large systems are reordered and interpreted as a space-only problem leading to multigrid algorithm with semi-coarsening in space and line smoothing in time direction. The smoother is further improved by embedding it as a preconditioner in a Krylov subspace method. As a prototypical application, we concentrate on scalar partial differential equations (PDEs) with up to many thousands of time steps which are discretized in time, resp., space by finite difference, resp., finite element methods. For linear PDEs, the resulting method is closely related to multigrid waveform relaxation and its theoretical framework. In our parabolic test problems the numerical behavior of this multigrid approach is robust w.r.t. the spatial and temporal grid size and the number of simultaneously treated time steps. Moreover, we illustrate how corresponding time-simultaneous fixed-point and Newton-type solvers can be derived for nonlinear nonstationary problems that require the described solution of linearized problems in each outer nonlinear step. As the main result, we are able to generate much larger problem sizes to be treated by a large number of cores so that the combination of the robustly scaling multigrid solvers together with a larger degree of parallelism allows a faster solution procedure for nonstationary problems.

Free Convective Flow of Water/Ethylene Glycol Based Micropolar Nanofluid Over a Shrinking Sheet

In this article, the free convective micropolar nanofluid was investigated over a shrinking sheet in the presence of a heat source by tacking into the water/ethylene glycol-based nanofluid account. The physical problem is first modeled. Under the assumptions of Boussinesq's approximation, the governing equations are reduced into non-linear PDEs. The combined non-linear PDEs representing momentum and non-homogeneous heat equations were reduced to a series of regular non-linear differential equations with appropriate similarity transformations. By applying the Runge-Kutta procedure followed by the Shooting technique, the transformed equations are then solved. Via the diagrams, the impact of related parameters characterizing the flow was presented and then addressed. It is observed that volumetric fraction has a substantial influence on the velocity profile and also induces a decrease in the boundary layer because water-based nanofluid has high thermal conductivity relative to Ferro nanofluid based on ethylene glycol.