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NON-OVERLAPPING RECTANGULAR DOMAIN DECOMPOSITION METHOD FOR TWO-DIMENSIONAL TELEGRAPH EQUATIONS

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초록

In this paper, a non-overlapping rectangular domain decom- position method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Nu- merical experiments of examples are compared with several methods.

Abstract

In this paper, a non-overlapping rectangular domain decom- position method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Nu- merical experiments of examples are compared with several methods.

참고문헌 (13)

  1. W.F. Ames, "Numerical methods for partial differential equations" (1992), Academic Press
  2. M. Asif, "A Haar wavelet collocation approach for solving one and two-dimensional second-order linear and nonlinear hyperbolic telegraph equations", Numer. Methods Partial Differential Equations, 36, pp.1962~1981 (2020)
  3. M. Aslefallah, "Application of the singular boundary method to the twodimensional telegraph equation on arbitrary domains", J. Engrg. Math, 118, pp.1~14 (2019)
  4. R.L. Burden, "Numerical Analysis", pp.2005, Thomson Brooks
  5. D. Haghighi, "The Fragile Points Method(FPM)to solve two-dimensional hyperbolic telegraph equation using point stiffness matrices", Eng. Anal. Bound. Elem, 134, pp.11~21 (2022)
  6. E. Hesameddini, "A new spectral Galerkin method for solving the two dimensional hyperbolic telegraph equation", Comput. Math. Appl, 72, pp.1926~1942 (2016)
  7. 전윤배, "Efficiency Analysis of a Domain Decomposition Method for the Two-dimensional Telegraph Equations", East Asian Mathematical Journal, 37(3), pp.295~305 (2021), 영남수학회
  8. J. Lin, "An accurate meshless collocation technique for solving two-dimensional hyperbolic telegraph equations in arbitrary domains", Eng. Anal. Bound. Elem, 108, pp.372~384 (2019)
  9. "MATHWORKS, Inc"[URL]
  10. R.C. Mittal, "A numerical study of two dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method", Appl. Math. Comput, 244, pp.976~997 (2014)
  11. R. K. Mohanty, "An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensions", Appl. Math. Comput, 152, pp.799~806 (2004)
  12. D.M. Young, "Iterative Solution of Large Linear Systems" (2003), Dover
  13. Z. Zhao, "Analysis of a continuous Galerkin method with mesh modification for two-dimensional telegraph equation", Comput. Math. Appl, 79, pp.588~602 (2020)

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