The aim of this paper was to accurately estímate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the T-estimation procedure, which aims to compare the residuals on a sequence of grids with different sp...

The diffraction grating problem is modeled by a boundary value problem governed by a Helmholtz equation with transparent boundary conditions. An a posteriori error estimate is derived when the truncation of the nonlocal boundary operators takes place. To overcome the difficulty caused by the fact that the truncated Dirichlet-to-Neumann (DtN) mapping does not converge to the original DtN mapping...

We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths, the truncation of both the number of modes and the local Hilbert-space dimensions is necessary. We derive superexponential Lieb-Robinson-type bounds on the error when restricting the bath to finitely ...

In this research, a numerical algorithm is employed to investigate the classical Blasius equation which is the governing equation of boundary layer problem. The base of this algorithm is on the development of RCW (Rahmanzadeh-Cai-White) method. In fact, in the current work, an attempt is made to solve the Blasius equation by using the sum of Taylor and Fourier series. While, in the most common ...

The a-posteriori error evaluation based on differential approximation of a finite-difference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Largange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic bound...

Difference representations on curvilinear coordinate systems are constructed by first transforming derivatives with respect to cartesian coordinates into expressions involving derivatives with respect to the curvilinear coordinates (the metric coefficients). The derivatives with respect to the curvilinear coordinates are then replaced with difference expressions on the uniform grid in the trans...