ON COMPACT 4TH ORDER FINITE-DIFFERENCE SCHEMES FOR THE WAVE EQUATION
نویسندگان
چکیده
We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) n-dimensional nonhomogeneous wave equation, n? 1. Their construction is accomplished by both classical Numerov approach and alternative technique based on averaging together with further necessary improvements arising scheme 2. The applicable to other types PDEs including parabolic time-dependent Schro¨dinger ones. are implicit three-point in each spatial direction time include a splitting operator For n = 1 mesh characteristics, becomes explicit close exact four-point scheme. present conditional stability theorem covering cases strong weak energy norms respect initial functions free term equation. Its corollary ensures error bound case smooth solutions IBVP. main generalized non-uniform rectangular meshes. also give results numerical experiments showing sensitive dependence orders three smoothness essential advantages over 2nd non-smooth as well.
منابع مشابه
High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations
In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...
متن کاملA Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation
We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson’s equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson’s equation on a compact st...
متن کاملHigh Order Compact Finite Difference Schemes for the Helmholtz Equation with Discontinuous Coefficients
In this paper, thirdand fourth-order compact finite difference schemes are proposed for solving Helmholtz equations with discontinuous media along straight interfaces in two space dimensions. To keep the compactness of the finite difference schemes and get global high order schemes, even at the interface where the wave number is discontinuous, the idea of the immersed interface method is employ...
متن کاملFourth-order and Optimised Finite Difference Schemes for the 2-d Wave Equation
This paper investigates some fourth-order accurate explicit finite difference schemes for the 2-D wave equation obtained using 13-, 17-, 21-, and 25-point discrete Laplacians. Optimisation is conducted in order to minimise numerical dispersion and computational costs. New schemes are presented that are more computationally efficient than nine-point explicit schemes at maintaining less than one ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2021
ISSN: ['1648-3510', '1392-6292']
DOI: https://doi.org/10.3846/mma.2021.13770