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Three-Point Difference Schemes of High Order of Accuracy for the Sturm–Liouville Problem
For the Sturm–Liouville problem, we construct three-point difference schemes of high order of accuracy on a nonuniform grid. The proposed difference...
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Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems
AbstractSeismic wave propagation through geological media is described by linear hyperbolic systems of equations. They correspond to acoustic,...
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Actual Accuracy of Linear Schemes of High-Order Approximation in Gasdynamic Simulations
AbstractA new test problem for one-dimensional gas dynamics equations is considered. Initial data in the problem is a periodic smooth wave. Shock...
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A High-Order Accuracy Method for Calculating the Initial Icing Stage of a Civil Aircraft’s Structural Elements
AbstractAn effective approach based on the discontinuous Galerkin method (DGM) of a high-order accuracy for calculating the initial stage of an...
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The Compact and Accuracy Preserving Limiter for High-Order Finite Volume Schemes Solving Compressible Flows
In this paper, a new limiter namely the compact weighted biased average procedure (CWBAP) is proposed for the shock capturing of high-order finite...
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Accuracy-Enhancement of Discontinuous Galerkin Methods for PDEs Containing High Order Spatial Derivatives
In this paper, we consider the accuracy-enhancement of discontinuous Galerkin (DG) methods for solving partial differential equations (PDEs) with...
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Improving the Accuracy
As mentioned previously, the FE method derived in Chapter 1 is not the most sophisticated ODE solver. Although it provides sufficient accuracy for...
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On the approximation of derivative values using a WENO algorithm with progressive order of accuracy close to discontinuities
In this article, we introduce a new WENO algorithm that aims to calculate an approximation to derivative values of a function in a non-regular grid....
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Fully Discrete Discontinuous Galerkin Numerical Scheme with Second-Order Temporal Accuracy for the Hydrodynamically Coupled Lipid Vesicle Model
In this paper, for the highly nonlinear hydrodynamically coupled elastic bending energy model of vesicle membranes, based on the discontinuous...
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Two structure-preserving schemes with fourth-order accuracy for the modified Kawahara equation
In this article, we present two high-order structure-preserving difference schemes for the modified Kawahara equation, which are named as Scheme I...
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On the Accuracy of Finite-Difference Schemes in Calculations of Centered Rarefaction Waves
AbstractA comparative accuracy analysis of three finite-difference schemes (the first order UpWind (UW), the second order TVD, and the third order in...
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On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves
AbstractA comparative experimental accuracy study of three shock-capturing schemes (the second-order CABARET, third-order Rusanov, and fifth-order in...
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Efficient Iterative Arbitrary High-Order Methods: an Adaptive Bridge Between Low and High Order
We propose a new paradigm for designing efficient p -adaptive arbitrary high-order methods. We consider arbitrary high-order iterative schemes that...
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Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves
AbstractWe perform a comparative analysis of the accuracy of the weighted essentially nonoscillatory (WENO), compact high-order weak approximation...
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On the second order of accuracy stable difference scheme for integral type non-local elliptic source identification problem
In this study, a source identification problem for elliptic differential equation with integral type non-local condition is discussed. The second...
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New Finite Difference Mapped WENO Schemes with Increasingly High Order of Accuracy
In this paper, a new type of finite difference mapped weighted essentially non-oscillatory (MWENO) schemes with unequal-sized stencils, such as the...
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Models: Interpretability, Accuracy, and Calibration
In this chapter, we present important concepts for when dealing with predictive models. We start with a discussion about the interpretability and...
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Assumptions and Accuracy Estimates
In this section, we prove the accuracy of our method, subject to some assumptions on the equation.