In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher's equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher's KPP equation.

To develop an efficient numerical scheme for two-dimensional convection diffusion equation using Crank-Nicholson and ADI, time-dependent nonlinear system is discussed. These schemes are of second order accurate in apace and time solved at each time level. The procedure was combined with Iterative methods to solve non-linear systems. Efficiency and accuracy are studied in term of 2 L , L ∞ norms confirmed by numerical results by choosing two test examples. Numerical results show that proposed alternating direction implicit scheme was very efficient and reliable for solving two dimensional nonlinear convection diffusion equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.

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In this research article, two finite difference implicit numerical schemes are described to approximate the numerical solution of the two-dimension modified reaction diffusion Fisher's system which exists in coupled form. Finite difference implicit schemes show unconditionally stable and second-order accurate nature of computational algorithm also the validation and comparison of analytical solution, are done through the examples having known analytical solution. It is found that the numerical schemes are in excellent agreement with the analytical solution. We found, second-implicit scheme is much faster than the first with good rate of convergence also we used NVIDA devices to accelerate the computations and efficiency of the algorithm. Numerical results show our proposed schemes with use of HPC (High performance computing) are very efficient and reliable.

The numerical solution of reaction diffusion systems may require more computational efforts if the change in concentrations occurs extremely rapid. This is because more time points are needed to resolve the reaction diffusion process accurately. In this paper, three finite difference implicit schemes are used which are unconditionally stable in order to enhance consistency. Novelty is reported by compact finite difference implicit scheme on a reaction diffusion system with higher accuracy measured by L 2 , L ∞ , and Relative error norms. Efficiency is observed by reducing grid space along small temporal steps. CPU performance, transmission capacity along comparison of three schemes shows excellent agreement with the analytical solution.INDEX TERMS Reaction diffusion systems, alternating direction implicit, Douglas scheme, higher order compact scheme, Thomas algorithm.

This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of 2 L , L ∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.

To develop an efficient numerical scheme for three-dimensional advection diffusion equation, higher order ADI method was proposed. 2nd and fourth order ADI schemes were used to handle such problem. Von Neumann stability analysis shows that Alternating Direction Implicit scheme is unconditionally stable. The accuracy and efficiency of such schemes was depicted by two test problems. Numerical results for two test problems were carried out to establish the performance of the given method and to compare it with the others Typical methods. Fourth order ADI method were found to be very efficient and stable for solving three dimensional Advection Diffusion Equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.

Nanoparticles are useful in improving the efficiency of convective heat transfer. The current study addresses this gap by making use of an analogy between Al2O3 and γ-Al2O3 nanoparticles in various base fluids across a stretched sheet conjunction with f. Base fluids include ethylene glycol and water. We address, for the first time, the stagnation-point flow of a boundary layer of γ-Al2O3 nanofluid over a stretched sheet with slip boundary condition. Al2O3 nanofluids employ Brinkman viscosity and Maxwell’s thermal conductivity models with thermal radiations, whereas γ-Al2O3 nanofluids use viscosity and thermal conductivity models generated from experimental data. For the boundary layer, the motion equation was solved numerically using the fourth-order Runge–Kutta method and the shooting approach. Plots of the velocity profile, temperature profile, skin friction coefficient and reduced Nusselt number are shown. Simultaneous exposure of the identical nanoparticles to water and ethylene glycol, it is projected, would result in markedly different behaviors with respect to the temperature profile. Therefore, this kind of research instills confidence in us to conduct an analysis of the various nanoparticle decompositions and profile structures with regard to various base fluids.