Quadrature Formulas for Oscillatory Integral Transforms.
Quadrature method for singular integral equations on closed curves.
Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed...
Regularisierung schlecht gestellter Probleme durch Projektionsverfahren.
Regularization properties of Tikhonov regularization with sparsity constraints.
Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...
Runge-Kutta Theory for Volterra Integrodifferential Equations
Semi-convergence and relaxation parameters for a class of SIRT algorithms.
Shannon wavelets for the solution of integrodifferential equations.
Simple square smoothing regularization operators.
Single-use reliability computation of a semi-Markovian system
Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first...
Smoothed projection methods for the moment problem.
Smoothing effect and regularity for evolution integrodifferential systems
SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions
MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).
Solution of Cauchy-type singular integral equations of the first kind with zeros of Jacobi polynomials as interpolation nodes.
Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets.
Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method.
Solution of nonlinear Volterra-Hammerstein integral equations via rationalized Haar functions.
Solution of the Undetermined Nonlinear Equations by Stationary Iteration Methods.
Solving a class of multivariate integration problems via Laplace techniques
We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...