LIAO Z P ， LIU J B. Numerical instabilities of a local transmitting boundary[J]. Earthquake Engineering & Structural Dynamics, 1992, 21(1): 65-77.？
[2]
LIAO Z P, ZHOU Z H ， ZHANG Y H. Stable implementation of transmitting boundary in numerical simulation of wave motion[J]. Chinese Journal of Geophysics, 2002, 45(4): 554-568.？
[3]
CRANK J,NICOLSON P.A practical method for numerical evaluation of solutions of partial differential equations of heat conduction type [J].Proc Cambridge Philos Soc， 1947，43： 50-67.？
[4]
HOFFMAN J D. Numerical methods for engineers and Scientists[M]. New York:McGraw-Hill Inc, 1992:657-691.？
[5]
HUGHES J R. Analysis of transient algorithms with particular reference to stability behavior[C]//Computational Methods for Transient Analysis.North-Holland:Elsevier Science, 1983: 67-155.？
[6]
GODUNOV S,RYABENKII V. Spectral stability criteria for boundary value problems for non-self-adjoint difference equations[J]. Russian Mathematical Surveys, 1963, 18(3): 1-12.？
[7]
KREISS H O. Stability theory for difference approxim- ations of mixed initial boundary value problems[J]. Mathematics of Computation, 1968, 22(104): 703-714.？
[8]
GUSTAFSSON B, KREISS H O,SUNDSTR？M A. Stability theory of difference approximations for mixed initial boundary value problems[J].Mathematics of Computation, 1972, 26(119): 649-686.？
[9]
GUSTAFSSON B, KREISS H O,OLIGER J.Time dependent problems and difference methods[M]. New York:John Wiley & Sons, 1995:496-620.？
[10]
TREFETHEN L.Group velocity interpretation of the stab- ility theory of Gustafsson, Kreiss and Sundstr[J].Journal of Computational Physics, 1983, 49(2): 199-217.？
[11]
STRIKWERDA J C. Finite difference schemes and partial differential equations [M].2nd ed.[S.1]:SIAM, 2004:1-34.？
[12]
RICHTMYER R D,MORTON K W.Difference methods for initial-value problems[M].2nd ed.New York:Interscience, 1967:39-58.？
[13]
STRIKWERDA J C,WADE B A. A survey of the Kreiss matrix theorem for power bounded families of matrices and its extensions, in linear operators[C]//Linear Operators. Warszaw:Inst Math Pol Acad Sciences, 1997: 329-360.？
[14]
PARTER S V.Stability,convergence,and pseudo-stability of finite-difference equations for an over-determined problem[J].Numerische Mathematik, 1962,4(1):277- 292.？
[15]
关慧敏,廖振鹏.局部人工边界稳定性的一种分析方法[J].力学学报, 1996, 28(3): 376-380.？ GUAN H M,LIAO Z P.A method for the stablitity analysis of local artificial boundaries[J]. Acta Mechanica Sinica, 1996, 28(3): 376-380.？
[16]
SOUSA E. On the edge of stability analysis[J]. Applied Numerical Mathematics, 2009, 59(6),1322-1336.？
[17]
谢志南,廖振鹏.波动方程数值模拟的一种显式方法-界面节点递推公式的构建[J].力学学报， 2011，43(1): 154-161.？ XIE Z N,LIAO Z P.An explicit method for numerical simulation of wave motion-constructing recursion formula for interface point[J].Acta Mechanica Sinica, 2011, 43(1): 154-161.？
[18]
廖振鹏，刘恒,谢志南. 波动数值模拟的一种显式方法――维波动[J].力学学报， 2009，41(3): 350-360.？ LIAO Z P,LIU H,XIE Z N.An explicit method for numerical simulation of wave motion:1-D wave motion[J].Acta Mechanica Sinica, 2009, 41(3): 350-360.？
[19]
HAIRER E, N？RSETT S P， WANNER G. Solving ordinary differential equations I:nonstiff problems[M].2nd ed. Berlin:Springer, 1993:80-89.？
[20]
DUPONT T. L2-estimates for Galerkin methods for seco- nd order hyperbolic equations[J].SIAM Journal on Numerical Analysis, 1972, 10(5): 880-889.？
[21]
GEKELER E. Linear multistep methods for stable diffe- rential equations[J].Mathematics of Computation,1982, 39(60): 481-490.
