Related papers: Piecewise orthogonal collocation for computing per…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
In this paper, an easy-to-implement and computationally effective numerical method based on the new orthogonal hybrid functions is developed to solve system of fractional order differential equations numerically. The new orthogonal hybrid…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
This paper introduces the Partition Tree Weighting technique, an efficient meta-algorithm for piecewise stationary sources. The technique works by performing Bayesian model averaging over a large class of possible partitions of the data…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
Starting with some fundamental concepts, in this article we present the essential aspects of spectral methods and their applications to the numerical solution of Partial Differential Equations (PDEs). We start by using Lagrange and…
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly…