Convergence of a second-order scheme for semilinear hyperbolic equations in dimensions

Authors:
Robert Glassey and Jack Schaeffer

Journal:
Math. Comp. **56** (1991), 87-106

MSC:
Primary 65M12; Secondary 35L70

DOI:
https://doi.org/10.1090/S0025-5718-1991-1052095-5

MathSciNet review:
1052095

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A second-order energy-preserving scheme is studied for the solution of the semilinear Cauchy Problem . Smooth data functions of compact support are prescribed at . On any time interval [0, *T*], second-order convergence (up to logarithmic corrections) to the exact solution is established in both the energy and uniform norms.

**[1]**J. Ginibre and G. Velo,*The global Cauchy problem for the nonlinear Klein-Gordon equation*, Math. Z.**189**(1985), 487-505. MR**786279 (86f:35149)****[2]**R. Glassey,*An elementary proof of time decay for solutions to semilinear wave equations in low space dimension*, Brown University LCDS Report #82-24, 1982.**[3]**R. Glassey, E. Horst, A. Lenard, and J. Schaeffer,*On the inverse of the discrete two-dimensional wave operator at CFL*, Preprint. MR**1129410 (93k:65069)****[4]**R. Glassey and H. Pecher,*Time decay for nonlinear wave equations in two space dimensions*, Manuscripta Math.**38**(1982), 387-400. MR**667924 (84a:35028)****[5]**E. Isaacson and H. B. Keller,*Analysis of numerical methods*, Wiley, New York, 1966. MR**0201039 (34:924)****[6]**W. Magnus, F. Oberhettinger, and R. P. Soni,*Formulas and theorems for the special functions of mathematical physics*, Springer-Verlag, New York, 1966. MR**0232968 (38:1291)****[7]**W. Strauss,*Nonlinear wave equations*, CBMS Lectures, George Mason University, January, 1989. MR**1032250 (91g:35002)****[8]**W. Strauss and L. Vasquez,*Numerical solution of a nonlinear Klein-Gordon equation*, J. Comput. Phys.**28**(1978), 271-278. MR**0503140 (58:19970)****[9]**L. Vasquez and G. Benyu,*A numerical scheme for nonlinear Klein-Gordon equations*, Chinese J. Appl. Sci.**1**(1983), 25-32.

Retrieve articles in *Mathematics of Computation*
with MSC:
65M12,
35L70

Retrieve articles in all journals with MSC: 65M12, 35L70

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1052095-5

Article copyright:
© Copyright 1991
American Mathematical Society