The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo appr...

A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucke...

A novel approach to solving the optimal nonlin-ear control problem is presented. Instead of seeking a global approximation to the Hamilton-Jacobi-Bellman equation, a local approximation is obtained by successively solving the Generalized Hamilton-Jacobi-Bellman (GHJB) equation on a local region of the state space. The optimal control is generated by solving the GHJB equation algebraically at se...

The paper proposed to use recurrent Fuzzy-Neural Multi-Model (FNMM) identifier for decentralized identification of a distributed parameter anaerobic wastewater treatment digestion bioprocess, carried out in a fixed bed and a recirculation tank. The distributed parameter analytical model of the digestion bioprocess is used as a plant data generator. It is reduced to a lumped system using the ort...

Two methods are presented for approximating the costate of optimal control problems in integral form using orthogonal collocation at Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) points. It is shown that the derivative of the costate of the continuous-time optimal control problem is equal to the negative of the costate of the integral form of the continuous-time optimal control problem. Us...

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...

In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary valu...