This work proposes a novel mesh free evolutionary Padé approximation (EPA) framework for obtaining closed form numerical solution of a nonlinear dynamical continuous model of virus propagation in computer networks. The proposed computational architecture of EPA scheme assimilates a Padé approximation to transform the underlying nonlinear model to an equivalent optimization problem. Initial conditions, dynamical positivity and boundedness are dealt with as problem constraints and are handled through penalty function approach. Differential evolution is employed to obtain closed form numerical solution of the model by solving the developed optimization problem. The numerical results of EPA are compared with finite difference schemes like fourth order Runge–Kutta (RK-4), ODE45 and Euler methods. Contrary to these standard methods, the proposed EPA scheme is independent of the choice of step lengths and unconditionally converges to true steady state points. An error analysis based on residuals witnesses that the convergence speed of EPA is higher than a globally convergent non-standard finite difference (NSFD) scheme for smaller as well as larger time steps.

This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system of ordinary differential equations involving ten dimensionless parameters by using similarity transformations. In the proposed EPA framework, an equivalent constrained optimization problem is formed. The solution of the resulting optimization problem is analogous to the solution of the dimensionless system of ordinary differential equations. The solutions produced in this work, with respect to various combinations of the physical parameters, are found to be in good agreement with those reported in the previously published literature. The effects of a non-dimensional physical-parameter wedge, Casson fluid, fluid phase effective heat capacity, Brownian motion, thermophoresis, radiation, and magnetic field on velocity profile, temperature profile, fluid concentration profile, and the density of motile microorganisms are discussed and presented graphically. It is observed that the fluid velocity rises with a rise in the Casson fluid viscosity force parameter, and an increase in the Prandtl number causes a decrease in the heat transfer rate. Another significant observation is that the temperature and fluid concentration fields are greatly increased by an increase in the thermophoresis parameter. An increase in the Péclet number suppresses the microorganism density. Moreover, the increased values of the Prandtl number increase the local Nusslet number, whereas the skin friction is increased when an increase in the Prandtl number occurs.

Dengue fever epidemic is an important infectious disease causing significant casualties and socioeconomic losses around the globe. There is an enormous pressure on public health policy makers for deriving standard guidelines and making effective decisions to safeguard the public from the dengue hazards. Mathematical modeling of dengue disease helps the decision-makers in understanding the disease dynamics and halting its spreading. This work introduces an innovative evolutionary computing and Padѐ rational approximation-based hybrid meshfree approach for analyzing the dynamical diffusion of dengue fever disease involving incubation epoch of virus. The proposed framework employs Padѐ approximation, penalty function approach, Nelder–Mead simplex (NMS) algorithm, and differential evolution (DE) to model and solve an equivalent optimization problem. The resulting method is named as differential cooperative multi-simplex Padѐ approximation (DCMP) scheme. The underlying dynamical model is analyzed for stabilities of its steady states. It is also shown that the proposed DCMP scheme possesses fast unconditional convergence, and preserves boundedness and positivity of the solution. Unlike the Euler (EU) and fourth-order Runge–Kutta (RK4) methods, the developed DCMP scheme is independent of discretization step length. The comparisons of results of DCMP with nonstandard finite difference scheme (NSFD) conform that the proposed DCMP truly exhibits the dynamics of the considered dengue disease model, involving incubation period of virus.

This study suggests a novel cooperative multi-simplex algorithm that generalizes a local search optimizer to design a novel global search heuristic algorithm. The proposed algorithm exploits the vertex sharing strategy to enhance the search abilities of the working simplexes. The vertex sharing among the simplexes is carried out through cooperative step that is based on fitness of the underlying simplex. The proposed algorithm is applied to solve some systems of nonlinear equations by transforming them to optimization problems. Comparative analysis of results shows that the proposed method is practical and effective.