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• We developed a powerful simulation framework to desynchronize the distribution of a network of uncoupled and noise-free (or noisy) neural oscillator populations. • The control model works based on the neurons phase distributions. • The PDEs of the control model is solved by fast and precise numerical methods. • Simulation carried out show the methods implemented in this paper are highly accurate, fast, and reliable in the presence of noise. Since control of synchronization at the onset of seizure can be considered an effective method of preventing or treating epilepsy, developing an advanced and accurate numerical simulation approach to implement control on noise-free (or noisy) population of synchronized neurons makes the control performance more effective. In this paper, we simulate a control by two powerful, fast and accurate meshless methods, i.e. compactly supported radial basis function collocation (CS-RBF) and radial basis function generated finite difference (RBF-FD) approaches, which enable us to realize new control objectives. It should be noted that the challenges faced by this model include the diverse behavior of neuronal populations, the speed of action in synchronization control, the minimization of energy consumption and the applicability of controlling real data, we show that the both proposed meshfree methods solve all these challenges. In addition, the evaluation of both methods by different phase response curves (PRC) as well as in the presence of Gaussian white noise shows that these methods can be implemented in experimental cases. The analyses and numerical results presented eventually confirm these claims. [ABSTRACT FROM AUTHOR]

• Numerical analysis of the shear banding phenomenon in two dimensions is performed. • Finite volume method for numerical simulation of shear banding processes is proposed. • The governing equations describe the shear banding process are derived on the basis of the modification of a hypoelastic Wilkins model. • The efficiency and accuracy of the proposed numerical algorithm is shown on three benchmark problems. • Self-organization processes of shear banding is studied. The aim of this paper is to develop an effective finite volume method for numerical simulation of the adiabatic shear bands (ASB) formation processes. A formation of ASB happens at high-speed shear strains of ductile materials. A numerical simulation of such problems using Lagrangian approach is associated with some problems, the main one of which is a mesh distortion at large deformations. We use Eulerian approach to describe a motion of the non-linear elasto-plastic material. More specifically, we consider a modification of a well-known hypoelastic Wilkins model. In this paper we suggest a numerical method for modeling of high-speed shear deformations on two-dimensional meshes. The method is verified on the three test problems suggested by other authors. [ABSTRACT FROM AUTHOR]

Based on the previous literature about the random logistic and Gompertz models, the aim of this paper is to extend the investigations to the generalized logistic differential equation in the random setting. First, this is done by rigorously constructing its solution in two different ways, namely, the sample-path approach and the mean-square calculus. Secondly, the probability density function at each time instant is derived in two ways: by applying the random variable transformation technique and by solving the associated Liouville's partial differential equation. It is also proved that both the stochastic solution and its density function converge, under specific conditions, to the corresponding solution and density function of the logistic and Gompertz models, respectively. The investigation finishes showing some examples, where a number of computational techniques are combined to construct reliable approximations of the probability density of the stochastic solution. In particular, we show, step-by-step, how our findings can be applied to a real-world problem. • The generalized logistic model with randomness is fully studied. • Uncertainty considered in all input parameters with arbitrary distributions. • RVT and Liouville PDE are applied to determine the 1-PDF under general assumptions. • Theoretical results are applied to a biological real-world problem. • PSO and Maximum Entropy used to fit the model to real data. • Wavelet-based AMR and lagrangian PDE methods combined to compute the 1-PDF. [ABSTRACT FROM AUTHOR]

The design, analysis and numerical simulations of a stabilized variable time-stepping difference scheme, for the Swift–Hohenberg equation, are considered in this paper. The proposed time-stepping scheme is proved to preserve a discrete energy dissipation law. With the help of the new discrete orthogonal convolution kernels, the unique solvability and the unconditional energy stability of the numerical scheme are rigorously proved. In addition, the second-order L 2 norm convergence both in time and in space, of the proposed scheme, is shown under the almost independent of the time-step ratios. To the best of our knowledge, this is the first time that the L 2 norm convergence of the adaptive BDF2 method is achieved for the Swift–Hohenberg equation. Numerical examples are provided to illustrate our theoretical results and to show the computational efficiency of the numerical scheme. • A stabilized variable time-stepping scheme for the Swift-Hohenberg equation is developed. • The theoretical results of the time-stepping scheme are rigorously proved. • The proposed adaptive time-stepping algorithms are suitable for the long time simulation. [ABSTRACT FROM AUTHOR]