Discretizing systems of nonlinear algebraic differential equations yield polynomial systems. When using a fine discretization, the resulting polynomial system is often too large to solve using a direct solving approach. Our approach for solving such systems is to utilize a homotopy continuation based method arising from domain decomposition. This method solves polynomial systems arising from su...

Abstract In this paper, we focus on the two-dimensional linear Telegraph equation with some initial and boundary conditions. We transform the model of partial differential equation (PDE) into a system of first order, linear, ordinary differential equations (ODEs). Our method is based on finding a solution in the form of a polynomial in three variables Un(x, y, t) = ∑n i=0 ∑n j=0 ∑n k=0 U(i, j, ...

A common problem in nonlinear control is the need to consider systems of high complexity. Here we consider systems, which although may be low order, have high complexity due to a complex right hand side of a differential equation (e.g. a right hand side which has many terms – such systems arise from coordinate transformations in constructive nonlinear control designs). This contribution develop...

Inelastic H(2):He collisions are studied from the experimental and theoretical points of view between 22 and 180 K. State-to-state cross sections and rates are calculated at the converged close-coupling level employing recent potential energy surfaces (PES): The MR-PES [J. Chem. Phys. 100, 4336 (1994)], and the MMR-PES and BMP-PESs [J. Chem. Phys. 119, 3187 (2003)]. The fundamental rates k(2-->...