Related papers: A product integration rule on equispaced nodes for…
We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand is assumed to be stationary. Requiring the integrand to…
We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate…
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…
This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and…
The numerical evaluation of integrals of the form \begin{align*} \int_a^b f(x) e^{ikg(x)}\,dx \end{align*} is an important problem in scientific computing with significant applications in many branches of applied mathematics, science and…
In this paper we revisit some quadrature methods for highly oscillatory integrals of the form $\int_{-1}^1f(x)e^{{\rm i}\omega x}dx, \omega>0$. Exponentially Fitted (EF) rules depend on frequency dependent nodes which start off at the…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…
In this paper we propose and analyse composite Filon-Clenshaw-Curtis quadrature rules for integrals of the form $I_{k}^{[a,b]}(f,g) := \int_a^b f(x) \exp(\mathrm{i}kg(x)) \rd x $, where $k \geq 0$, $f$ may have integrable singularities and…
The rich non-linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While…
In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established…
In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.
In this paper we suggest two modified one-point Gauss integration rules for the Q1 bi- or trilinear element. The modifications both stabilize the hourglass modes of the one-point rule, and one of them is accurate also on severely distorted…
This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…