Convergence of Two-Dimensional Nyström Discrete-Ordinates in Solving the Linear Transport Equation.
Convolution Quadrature and Discretized Operational Calculus. I.
Convolution Quadrature and Discretized Operational Calculus. II.
Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be...
Die Theorie der asymptotischen Verteilung und die numerische Lösung von Integrodifferentialgleichungen.
Direct methods for the solution of singular integral equations with finite number of different zeros in pairwise.
Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions
In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative () and integration matrix () are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...
Discrete Newton Methods and Iterated Defect Corrections.
Discretization of Volterra Integral Equations of the First Kind (II).
Duality Estimates for the Numerical Solution of Integral Equations.
Dynamical systems method for solving linear finite-rank operator equations
A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.
Dynamical systems method for solving linear ill-posed problems
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning the discrepancy principle for choosing the regularization parameter are obtained.
EasyMSG : tools and techniques for an adaptive overlapping in SPMD programming
During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this techniques...
EasyMSG: Tools and techniques for an adaptive overlapping in SPMD programming
During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this...
Efficient algorithms for solving nonlinear Volterra integro-differential equations with two point boundary conditions.
Efficient iterative solution of linear systems from discretizing singular integral equations.
Erratum: Spline qualocation methods for boundary integral equations.
Erratum to Numer. Math. 52, 219-240 (1988). Product Integration for the Linear Transport Equation in Slab Geometry.
Error Analysis for a Class of Degenerate-Kernel Methods.
Error analysis for the finite element approximation of a radiative transfer model