
Hybridized SummationByParts Finite Difference Methods
We present a hybridization technique for summationbyparts finite diffe...
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Instabilities and order reduction phenomenon of an interpolation based multirate RungeKuttaChebyshev method
An explicit stabilized additive RungeKutta scheme is proposed. The meth...
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A formal proof of the Lax equivalence theorem for finite difference schemes
The behavior of physical systems is typically modeled using differential...
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Singular integration towards a spectrally accurate finite difference operator
It is an established fact that a finite difference operator approximates...
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A dynamicallyconsistent nonstandard finite difference scheme for the SICA model
In this work, we derive a nonstandard finite difference scheme for the S...
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Error Bounds for a Least Squares Meshless Finite Difference Method on Closed Manifolds
We present an error bound for a least squares version of the kernel base...
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Convergence analysis of inexact twogrid methods: Multigrid cycles
Multigrid is a popular iterative solver for a large class of linear syst...
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Error Inhibiting Methods for Finite Elements
Finite Difference methods (FD) are one of the oldest and simplest methods used for solving differential equations. Theoretical results have been obtained during the last six decades regarding the accuracy, stability, and convergence of the FD method for partial differential equations (PDE). The local truncation error is defined by applying the difference operator to the exact solution u. In the classical FD method, the orders of the global error and the truncation error are the same. Block Finite Difference methods (BFD) are finite difference methods in which the domain is divided into blocks, or cells, containing two or more grid points with a different scheme used for each grid point, unlike the standard FD method. In this approach, the interaction between the different truncation errors and the dynamics of the scheme may prevent the error from growing, hence error reduction is obtained. The phenomenon in which the order of the global error is smaller than the one of the truncation error is called error inhibition It is worth noting that the structure of the BFD method is similar to the structure of the DG method as far as the linear algebraic system to be solved is concerned. In this method as well, the phenomenon of error inhibition may be observed. We first show that our BFD scheme can be viewed as a DG scheme, proving stability during the process. Then, performing a Fourier like analysis, we prove optimal convergence of the BFD scheme.
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