In this research we used forward-backward sweep method(FBSM) in order to solve optimal control problems. In this paper, one hybrid method based on ERK method of order 4 and 5 are proposed for the numerical approximation of the OCP. The convergence of the new method has been proved .This method indicate more accurate numerical results compared with those of ERK method of order 4 and 5 for solvin...

We establish the equivalence between Multiscale Hybrid-Mixed (MHM) and Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under idealized assumption that local problems defining multiscale basis functions are exactly solved, we prove holds general polytopal (coarse) meshes arbitrary approximation orders. also leverage interchange of propert...

Monte Carlo methods refer to any method that uses random numbers to get an approximate answer to a problem. In computer graphics Monte Carlo techniques can be used to perform radiosity calculations and can be used in distribution ray tracing for effects such as soft shadows and motion blur. Although these notes are for a course on radiosity, they have a great deal of material from a previous Si...

MULTISCALE–HYBRID–MIXED METHODS ALEXANDRE L. MADUREIRA Dedicated to Leo Franca, in memoriam. ABSTRACT. In an abstract setting, we investigate the basic ideas behind the Multiscale Hybrid Mixed (MHM) method, a Domain Decomposition scheme designed to solve multiscale partial differential equations (PDEs) in parallel. As originally proposed, the MHM method starting point is a primal hybrid formula...

This paper reports the development of a Matlab toolbox for computational analysis of piecewise linear systems. The analysis is based on piecewise quadratic Lyapunov functions, which are computed via convex optimization. In this way, exponential stability and system performance can be assessed. The toolbox also supports efficient simulation of systems with discontinuous dynamics and sliding mode...

Considering the strategic importance of coastal areas from various aspects, their protection against waves is a coast management necessity. Since long ago, strong coastal structures have protected coasts, but since they disturb the coastal ecosystem balance, effort has been made to use them less or make them more compatible with the coast. This research is specifically aimed to estimate the eff...