We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particu...

We present a formulation of rigid body dynamics with frictional contact that leverages ideas from discrete mechanics to derive time-stepping schemes with any desired order of integration accuracy. By utilizing the new time-stepping methods as dynamics constraints in a direct trajectory optimization scheme, we are able to perform contact-implicit trajectory optimization with accuracy equal to tr...

We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known...

Dynamic range is a critical gure of merit for image sensors. Often a sensor with higher dynamic range is regarded as higher quality than one with lower dynamic range. For CCD and CMOS sensors operating in the integration mode the sensor SNR monotonically increases with the signal. Therefore, a sensor with higher dynamic range, generally, produces higher quality images than one with lower dynami...

The primary objective of this thesis is to seek a ground-based location scheme suitable for mobile positioning in cellular phone networks. To this end, several techniques are proposed to handle issues that may occur in a cellular network and which may deteriorate wireless location performance. These issues include the lack of signal availability due to co-channel interference, the inefficiency ...

This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints ...

The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge-Kutta schemes and computing the max...

We consider the numerical integration of the Degasperis–Procesi equation, which was recently introduced as a completely integrable shallow water equation. For the equation, we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi-Hamiltonian form of the equation at a same time. We also prove the unique solvability of the schemes, and show som...

The numerical integration in time of the equations of motion for mechanical systems subject to holonomic constraints is considered. Schemes are introduced for the direct treatment of a diierential-algebraic form of the equations that preserve the constraints, the total energy, and other integrals such as linear and angular momentum arising from aane symmetries. Moreover, the schemes can be show...

Distillation column is one of the most common operations in process industries and is while the most expensive unit of the amount of energy consumption. Many ideas have been presented in the related literature for optimizing energy consumption in distillation columns. This paper studies the different heat integration methods in a distillation column which separate Benzene, Toluene, Xylene, and ...