The paper proposed to use a Recurrent Neural Network Model (RNNM) and a dynamic Backpropagation learning for centralized identification of an anaerobic digestion bioprocess, carried out in a fixed bed and a recirculation tank of a wastewater treatment system. The anaerobic digestion bioprocess represented a distributed parameter system, described by partial differential equations. The analytica...

In this paper we present the theoretical framework needed to justify the use of a kernelbased collocation method (meshfree approximation method) to estimate the solution of highdimensional stochastic partial differential equations (SPDEs). Using an implicit time stepping scheme, we transform stochastic parabolic equations into stochastic elliptic equations. Our main attention is concentrated on...

In this paper, an algorithm based on the collocation and homotopy analysis methods, for solving initial-boundary value problems, is introduced. The application of this algorithm is based on the approximation and interpolation of the dependent variables by using suitable functions or polynomials according to their values in the collocation points corresponding to a suitable discretization of the...

A research code has been written to solve an elliptic system of coupled nonlinear partial differential equations of conservation form on a rectangularly shaped three-dimensional domain. The code uses the method of collocation of Gauss points with tricubic Hermite piecewise continuous polynomial basis functions. The system of equations is solved by iteration. The system of nonlinear equations is...

We introduce a novel technique of uncertainty quantification using polynomial regression with derivative information and apply it to analyze the performance of a model of a sodium-cooled fast reactor. We construct a surrogate model as a goal-oriented projection onto an incomplete space of polynomials, find coordinates of projection by collocation, and use derivative information to reduce the nu...

In this paper, a simple transformation of coordinates is proposed that facilitates the efficient simulation of the non-isothermal lithium-ion pseudo 2-D battery model. The transformed model is then conveniently discretized using orthogonal collocation with the collocation points in the spatial direction. The resulting system of differential algebraic equations (DAEs) is solved using efficient a...

A reduction method is presented for systems of conservation laws with boundary energy flow. It is stated as a generalized pseudo-spectral method which performs exact differentiation by using simultaneously several approximation spaces generated by polynomials bases and suitable choices of port-variables. The symplecticity of this spatial reduction method is proved when used for the reduction of...

In this paper we investigate collocation methods for the computation of periodic solutions of autonomous delay diierential equations (DDEs). Periodic solutions are found by solving a periodic two-point boundary value problem, which is an innnite-dimensional problem for DDEs, in contrast to the case of ordinary diierential equations. We investigate three collocation methods based on piecewise po...

In this paper we present a method based on using exponential basis functions (EBFs) to solve well-known two-dimensional time dependent engineering problems such as elasto-dynamic ones. The formulation has much in common with those in three dimensional problems while time is taken as the third axis. The solution is first approximated by a summation of EBFs and then completed by satisfying the ti...