A variant of Newton's method for the computation of traveling waves of bistable differential-difference equations

被引：50
作者：
Elmer C.E. [1 ]
Van Vleck E.S. [2 ]
机构：
[1] Department of Mathematical Sciences, New Jersey Institute of Technology, Newark
[2] Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden
来源：
Journal of Dynamics and Differential Equations | 2002年 / 14卷 / 3期
基金：
美国国家科学基金会;
关键词：
Mixed type functional differential equations; Newton's method; Traveling waves;
D O I：
10.1023/A:1016386414393
中图分类号：
学科分类号：
摘要：
We consider a variant of Newton's method for solving nonlinear differential-difference equations arising from the traveling wave equations of a large class of nonlinear evolution equations. Building on the Fredholm theory recently developed by Mallet-Paret we prove convergence of the method. The utility of the method is demonstrated with a series of examples. © 2002 Plenum Publishing Corporation.
引用
收藏
页码：493 / 517
页数：24
相关论文
共 43 条
  • [11] Chi H., Bell J., Hassard B., Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory, J. Math. Biol., 24, pp. 583-601, (1986)
  • [12] Chow S.-N., Shen W., Stability and bifurcation of traveling wave solutions in coupled map lattices, Dynam. Systems Appl., 4, pp. 1-26, (1995)
  • [13] Doedel E.J., Friedman M.J., Numerical computation of heteroclinic orbits, J. Comput. Appl. Math., 25, pp. 155-171, (1989)
  • [14] Elmer C.E., Van Vleck E.S., Computation of traveling wave solutions for spatially discrete bistable reaction-diffusion equations, Appl. Numer. Math., 20, pp. 157-169, (1996)
  • [15] Elmer C.E., Van Vleck E.S., Analysis and computation of traveling wave solutions of bistable differential-difference equations, Nonlinearity, 12, pp. 771-798, (1999)
  • [16] Elmer C.E., Van Vleck E.S., Traveling wave solutions of bistable differential-difference equations with periodic diffusion, SIAM J. Appl. Math., 61, pp. 1648-1679, (2001)
  • [17] Fath G., Propagation failure of traveling waves in a discrete bistable medium, Phys. D, 116, pp. 176-190, (1998)
  • [18] Fife P.C., Diffusive waves in inhomogeneous media, Proc. Edinburgh Math. Soc., 32, pp. 291-315, (1989)
  • [19] Fife P.C., Hsiao L., The generation and propagation of internal layers, Numer. Anal. TMA, 12, pp. 19-41, (1988)
  • [20] Fife P., McLeod J., The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rational Mech. Anal., 65, pp. 333-361, (1977)
12345