A Capacitance Matrix Method for Dirichlet Problem on Polygon Region.
A case where balancing is harmful.
A C...-Collocation-like Method for Two-Point Boundary Value Problems.
A center of a polytope: An expository review and a parallel implementation.
A central scheme for shallow water flows along channels with irregular geometry
We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
A central scheme for shallow water flows along channels with irregular geometry
We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
A central WENO-TVD scheme for hyperbolic conservation laws.
A certain class of quadratures.
A certain class of quadratures.
A certain class of quadratures with hat function as a weight function.
A certain integral-recurrence equation with discrete-continuous auto-convolution
Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.
A certified reduced basis method for parametrized elliptic optimal control problems
In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...
A challenging test for convergence accelerators: summation of a series with a special sign pattern.
A characterization of strong regularity of interval matrices.
A characterization of the approximation order for multivariate spline spaces
A Chebyshev-like semiiteration for inconsistent linear systems.
A class of combinatorial problems with polynomially solvable large scale set covering/partitioning relaxations
A Class of Direct Methods for Linear Systems.
A Class of Iterative Methods for Holomorphic Functions.
A Class of Iterative Methods for Solving Saddle Point Problems.