The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates Lp([0, T ]) and uniform approximations of φ-sub-Gaussian random processes by finite time sampling sums. Explicit truncation error upper bounds are established. Some specifications of the general results for wh...

Achieving improved order of accuracy for a hydrodynamic numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. This paper presents a weak statement perturbation methodology retaining block-tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to hi...

Uncertainty quantification plays an important role in problems that involve inferring a parameter of initial value problem from observations the solution. Conrad et al.\ (\textit{Stat.\ Comput.}, 2017) proposed randomisation deterministic time integration methods as strategy for quantifying uncertainty due to unknown discretisation error. We consider this systems are described by deterministic,...

We derive a sampling expansion for bandlimited signals with polynomial growth on the real axis. The sampling expansion uses nonuniformly spaced sampling points. But unlike other known sampling expansions for such signals, ours converge uniformly to the signal on any compact set. An estimate of the truncation error of such a series is also obtained.

Over the years, scholars have developed predictor-corrector method to provide estimates for ordinary differential equations (ODEs). Predictor-corrector methods been reduced predicting-correcting with no concern finding convergence-criteria each loop suitable vary step size in order maximize error. This study aim consider computing fuzzy employing extended block predictor-block corrector (EBP-BC...

The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered.The concept of variable order fractional derivative is considered in the sense of Caputo.The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presen...

The standard approach for integrating the multidimensional Vlasov equation using grid based, conservative schemes is based on a time splitting approach. Here, we show that although the truncation error is of second order, time splitting can introduce systematic heating of the plasma. We introduce a backsubstitution method, which not only avoids this deficiency but also is computationally less e...

This paper addresses the problem of outage characterization of an ambient backscatter communication system with a pair of passive tag and reader. In particular, an exact expression for the effective channel distribution is derived. Then, the outage probability at the reader is analyzed rigorously. Since the expression contains an infinite sum, a tight truncation error bound has been derived to ...

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can b...