바로가기메뉴

본문 바로가기 주메뉴 바로가기
 

logo

  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

Article Contents

Prev Next
e-Submission

Vol.17 No.4

PDF Citation Share

AN EFFICIENT SECOND-ORDER NON-ITERATIVE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC TELEGRAPH EQUATIONS

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2010, v.17 no.4, pp.289-298
Jun, Young-Bae
Hwang, Hong-Taek
Jun,, Y. , & Hwang,, H. (2010). AN EFFICIENT SECOND-ORDER NON-ITERATIVE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC TELEGRAPH EQUATIONS, 17(4), 289-298.

Abstract

In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.

keywords
second-order accuracy, domain decomposition, finite difference method, hyperbolic telegraph equation, unconditional stability

Reference

1.

Zhang, Zhiyue;Deng, Dingwen. (2007). A new alternating-direction finite element method for hyperbolic equation. Numerical Methods for Partial Differential Equations, 23(6), 1530-1559. 10.1002/num.20240.

2.

(2006). . J. Korea Soc. Math. Educ. Ser. B: Pure and Appl. Math., 13, 281-294.

3.

Ding, H.;Zhang, Y.. (2009). A new unconditionally stable compact difference scheme of O(&tau;<SUP>2</SUP>+h<SUP>4</SUP>) for the 1D linear hyperbolic equation. Applied Mathematics and Computation, 207(1), 236-241. 10.1016/j.amc.2008.10.024.

4.

Ramezani, Mehdi;Dehghan, Mehdi;Razzaghi, Mohsen. (2008). Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition. Numerical Methods for Partial Differential Equations, 24(1), 1-8. 10.1002/num.20230.

5.

Jun, Y.. (2009). An efficient domain decomposition method for three-dimensional parabolic problems. Applied Mathematics and Computation, 215(8), 2815-2825. 10.1016/j.amc.2009.09.022.

6.

SHARMA. (2008). . Applied Mathematics and Computation, 201(1-2), 229-238. 10.1016/j.amc.2007.12.051.

7.

Mohanty, R.K.. (2007). Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms. Applied Mathematics and Computation, 190(2), 1683-1690. 10.1016/j.amc.2007.02.097.

8.

Jun, Y.;Mai, T.Z.. (2006). ADI method - Domain decomposition. Applied Numerical Mathematics, 56(8), 1092-1107. 10.1016/j.apnum.2005.09.008.

9.

(2005). . Math. Comp., 74, 153-176.

10.

(2009). . SIAM J. Sci. Comput., 31, 4244-4265.

11.

Benito, J.J.;Urena, F.;Gavete, L.. (2007). Solving parabolic and hyperbolic equations by the generalized finite difference method. Journal of Computational and Applied Mathematics, 209(2), 208-233. 10.1016/j.cam.2006.10.090.

12.

Mohanty, R.K.. (2005). An unconditionally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficients. Applied Mathematics and Computation, 165(1), 229-236. 10.1016/j.amc.2004.07.002.

13.

Mohebbi, Akbar;Dehghan, Mehdi. (2008). High order compact solution of the one-space-dimensional linear hyperbolic equation. Numerical Methods for Partial Differential Equations, 24(5), 1222-1235. 10.1002/num.20313.

14.

Codina, R.. (2008). Finite element approximation of the hyperbolic wave equation in mixed form. Computer Methods in Applied Mechanics and Engineering, 197(13), 1305-1322. 10.1016/j.cma.2007.11.006.

15.

Liu, Y.;Li, H.. (2009). H<SUP>1</SUP>-Galerkin mixed finite element methods for pseudo-hyperbolic equations. Applied Mathematics and Computation, 212(2), 446-457. 10.1016/j.amc.2009.02.039.

16.

(1994). . Contemp. Math., 157, 45-52.

17.

18.

19.

Jun, Y.. (2010). A stable noniterative Prediction/Correction domain decomposition method for hyperbolic problems. Applied Mathematics and Computation, 216(8), 2286-2292. 10.1016/j.amc.2010.03.064.

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

e-Submission OA Policy