The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in so...

In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

We present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo-spectral methods. This problem is split into two parts. The first step is the determination of a suitable conformal factor which transforms from an initial data set in physical space-time to a hyperboloidal hypersurface in the ambient conformal manifold. This is achiev...

We study moving topological solitons (kinks and antikinks) in the nonlinear KleinGordon chain. These solitons are shown to exist with both monotonic (non-oscillating) and oscillating asymptotics (tails). Using the pseudo-spectral method, the (anti)kink solutions with oscillating background (so-called nanopterons) are found as travelling waves of permanent profile propagating with constant veloc...

It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a novel type of static kink solution which may occupy any position relative to the spatial lattice and experiences no Peierls-Nabarro barrier. Consequently the d...

This paper presents a numerical scheme for space fractional diffusion equations (SFDEs) based on pseudo-spectral method. In this approach, using the Guass-Lobatto nodes, the unknown function is approximated by orthogonal polynomials or interpolation polynomials. Then, by using pseudo-spectral method, the SFDE is reduced to a system of ordinary differential equations for time variable t. The hig...

A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrödinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref. [56] to prove that the optimal rate of convergence of the new method is in the order of O(N...

Efficient and safe battery charge control is an important prerequisite for large-scale deployment of clean energy systems. This paper proposes an innovative approach to devising optimally health-conscious fast-safe charge protocols. A multiobjective optimal control problem is mathematically formulated via a coupled electro-thermal-aging battery model, where electrical and aging sub-models depen...