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...

A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...

We introduce isogeometric collocation methods based on generalized B-splines and we analyze their performance through numerical examples for univariate and multivariate scalarand vector-valued problems. In particular, advection–diffusion and linear elasticity model problems are addressed. The resultingmethod combines the favorable properties of isogeometric collocation and the geometrical and a...

Title of dissertation: MESHLESS COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUED PROBLEMS AND THE ROTATIONAL SHALLOW WATER EQUATIONS ON THE SPHERE Christopher D. Blakely, Doctor of Philosophy, 2009 Dissertation directed by: Professor John Osborn Department of Mathematics Professor Ferdinand Baer Department of Atmospheric and Oceanic Science This dissertation thesis has...

Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of a-posteriori error estimation adaptive stepping proposed in Kopteva (2022). We improve earlier algorithm based on this theory, specifically address its stable efficient implementation context high-order methods. The considered methods includ...

This paper investigates the task of noun compound interpretation, building on the sense collocation approach proposed by Moldovan et al. (2004). Our primary task is to evaluate the impact of similar words on the sense collocation method, and decrease the sensitivity of the classifiers by expanding the range of sense collocations via different semantic relations. Our method combines hypernyms, h...

We describe a mesh selection strategy for the numerical solution of boundary value problems for singular ordinary differential equations. This mesh adaptation procedure is implemented in our MATLAB code sbvp which is based on polynomial collocation. We prove that under realistic assumptions our mesh selection strategy serves to approximately equidistribute the global error of the collocation so...