In this paper we propose a method for conducting stochastic collocation on arbitrary sets of nodes. To accomplish this, we present the framework of least orthogonal interpolation, which allows one to construct interpolation polynomials based on arbitrarily located grids in arbitrary dimensions. These interpolation polynomials are constructed as a subspace of the family of orthogonal polynomials...

Several numerical methods for approximating the solution of Hammerstein integral equations are known. For Fredholm-Hammerstein integral equations, the classical method of successive approximations was introduced in [16]. A variation of the Nystrom method was presented in [11]. A collocation-type method was developed in [9]. In [3], Brunner applied a collocation-type method to nonlinear Volterra...

In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...

The paper proposed to use decentralized and centralized I-term neural sliding mode control of distributed parameter wastewater anaerobic digestion bioprocess plant. The bioprocess plant is described by partial differential equations simplified by means of the orthogonal collocation method and used as an input/output data generator. The obtained process data are identified by means of decentrali...

In this article, a Takagi-Sugeno fuzzy observer for the anaerobic digestion process in a fluidized bed reactor is proposed. First, a general explanation of this bioprocess is introduced. A model of the system discretized in the space by the orthogonal collocation method is presented. This model is analyzed locally to prove properties of stability and observability. Then, the design of the fuzzy...

Non-linear diffusion and adsorption problems in heterogeneous systems are investigated in this study. Highly non-linear functions are proposed and are found necessary for the adequate representation of concentrationdependent diffusion coefficients in many practical heterogeneous diffusion and adsorption systems. The nonlinear differential equation governing the diffusion and absorption process ...

Stratégia adaptívneho riadenia pre triedu nelineárneho rozvoja bioprocesov This paper presents the control problem of a class of propagation bioprocesses that are carried out in fixed bed reactors. Since the dynamics of these processes are described by partial differential equations, in order to obtain useful models for control purposes, a possible method consists of approximation of their infi...

This paper investigates the state estimation of a high-fidelity spatially resolved thermalelectrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This im...