A new kind of double Chebyshev polynomial approximation on unbounded domains

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

Distributed Signal Processing via Chebyshev Polynomial Approximation

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We...

On the Oberbeck-Boussinesq approximation on unbounded domains

We study the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a general unbounded domain in R3. We provide a rigorous justification of the model by means of scale analysis of the full Navier-Stokes-Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Fin...

Chebyshev polynomial approximation for transductive learning on graphs

On the Solvability of a Class of Second Kind Integral Equations on Unbounded Domains

Ž . Ž . We consider integral equations of the form c x s f x q Ž . Ž . Ž . Ž . H k x, y z y c y dy in operator form c s f q K c , where V is some subset V z n Ž . Ž . of R n G 1 . The functions k, z, and f are assumed known, with z g L V and ` f g Y, the space of bounded continuous functions on V. The function c g Y is to be determined. The class of domains V and kernels k considered includes t...