相关论文: On the global error committed when evaluating the …
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
The paper is devoted to well-posedness analysis and the numerical solution of a family of general elliptic mixed variational-hemivariational inequalities. Various mixed variational equations, mixed variational inequalities and mixed…
This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE.…
Partial Wave Analysis has traditionally been carried out using a set of tools handcrafted for each experiment. By taking an object-oriented approach, the design presented in this paper attempts to create a more generally useful, and easily…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
With the immense computing power at our disposal, the numerical solution of partial differential equations (PDEs) is becoming a day-to-day task for modern computational scientists. However, the complexity of real-life problems is such that…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretisation errors…
Energy stable flux reconstruction (ESFR) is a high-order numerical method used for solving partial differential equations in computational fluid dynamics. This method is designed to preserve the energy stability of the underlying partial…
In this paper we investigate spectral stability of traveling wave solutions to 1-$D$ quantum hydrodynamics system with nonlinear viscosity in the $(\rho,u)$, that is, density and velocity, variables. We derive a sufficient condition for the…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
In this report we discuss the treatment of statistical errors in cut efficiencies. The two commonly used methods for the calculation of the errors, Poissonian and Binomial, are shown to be defective. We derive the form of the underlying…