We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence relevant finite-element provide theoretical estimate error. conclude with some numerical experiments further support results.

We compare a kernel-based collocation method (meshfree approximation method) with a Galerkin finite element method for solving elliptic stochastic partial differential equations driven by Gaussian noise. The kernel-based collocation solution is a linear combination of reproducing kernels obtained from related differential and boundary operators centered at chosen collocation points. Its random ...

A comparative study of weighted residual methods has been made on different types of advection diffusion equations. Both the linear and non-linear models have been discretized by orthogonal collocation method (OCM) and orthogonal collocation on finite elements (OCFE). Model equations have been solved by MATLAB ‘ode15s’ system solver. Numerical values have been compared with analytic ones and in...

Fast direct methods are presented for the solution of linear systems arising in highorder, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial di erential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline co...

Finite element method (FEM) is an efficient numerical tool for the solution of partial differential equations (PDEs). It one most general methods when compared to other techniques. PDEs posed in a variational form over given space, say Hilbert are better numerically handled with FEM. The FEM algorithm used various applications which includes fluid flow, heat transfer, acoustics, structural mech...

This paper presents the simultaneous solution of the optimal sequencing and optimal dynamic transitions of two multigrade polymerization CSTRs. The simultaneous formulation results in a Mixed-Integer Dynamic Optimization (MIDO) problem. The profiles of the state variables during dynamic transitions are discretized using orthogonal collocation on finite elements, transforming the MIDO problem in...

This contribution describes the development of various strategies for the dynamic optimization of a batch reactor in order to obtain a robust model, suitable for nonlinear (NLP) or mixed-integer nonlinear programming (MINLP) problems. Different Orthogonal Collocation on Finite Element (OCFE) schemes and various formulations of the MINLP model have been studied to increase its robustness. It has...

In this work we propose a scheduling and control formulation for simultaneously addressing scheduling and control problems by explicitly incorporating process dynamics in the form of system constraints that ought to be met. The formulation takes into account the interactions between such problems and is able to cope with nonlinearities embedded into the processing system. The simultaneous sched...