In this paper a Chebyshev collocation method is used for solving numerically an optimal boundary control problem in a thermoconvective fluid flow. The aim of this study is to demonstrate the capabilities of these numerical techniques for handling this kind of problems. As the problem is treated in the primitive variable formulation additional boundary conditions for the pressure and the auxilia...

A new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection– diffusion equation in the unbounded domain Rn is converted to one on the bounded domain [−1,1]n , and the Laplace transform is applied to eliminate time dependency. The consequent boundary value ...

The classical pseudospectral collocation method based on the expansion of solution in a basis Chebyshev polynomials is considered. A new approach to constructing systems linear algebraic equations for solving ordinary differential with variable coefficients and initial (and/or boundary) conditions makes possible significant simplification structure matrices, reducing it diagonal form. system re...

In this paper, the temporal development of small disturbances in magnetohydrodynamic (MHD) Jeffery–Hamel flows is investigated, in order to understand the stability of hydromagnetic steady flows in convergent/divergent channels at very small magnetic Reynolds number Rm . A modified form of normal modes that satisfy the linearized governing equations for small disturbance development asymptotica...

This article introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations, which achieves spectral accuracy smooth surfaces. The approach is based on hybrid Nyström-collocation using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, proposed strategy applied magnetic field (M...

The idea of `1-minimization is the basis of the widely adopted compressive sensing method for function approximation. In this paper, we extend its application to high-dimensional stochastic collocation methods. To facilitate practical implementation, we employ orthogonal polynomials, particularly Legendre polynomials, as basis functions, and focus on the cases where the dimensionality is high s...

The normal mode model is important in computational atmospheric acoustics. It often used to compute the acoustic field under a time-independent single-frequency sound source. Its solution consists of set discrete modes radiating into upper atmosphere, usually related continuous spectrum. In this article, we present two spectral methods, Chebyshev-Tau and Chebyshev-Collocation solve for modes, c...

We consider the construction of a special family of Runge–Kutta (RK) collocation methods based on intra-step nodal points of Chebyshev–Gauss–Lobatto type, with A-stability and stiffly accurate characteristics. This feature with its inherent implicitness makes them suitable for solving stiff initial-value problems. In fact, the two simplest cases consist in the well-known trapezoidal rule and th...

This paper presents an accurate and stable numerical scheme for computation of the first variation of the Dirichlet–Neumann operator in the context of Euler’s equations for ideal free-surface fluid flows. The Transformed Field Expansion methodology we use is not only numerically stable, but also employs a spectrally accurate Fourier/Chebyshev collocation method which delivers high-fidelity solu...