A Hermite spectral method for the computation of homoclinic orbits and associated functionals

• Published in: Journal of computational and applied mathematics Vol. 206; no. 2; pp. 986 - 1006
• Main Authors: Korostyshevskiy, Valeriy R., Wanner, Thomas
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-09-2007; Elsevier
• Subjects: Exact sciences and technology; Exponential convergence; Global analysis, analysis on manifolds; Hermite functions; Homoclinic orbits; Mathematical analysis; Mathematics; Metastability; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; Spectral methods; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; 34C37; Exponential convergence; 34B15; 41A30; Hermite functions; 65T99; Homoclinic orbits; 42C15; 65L10; Spectral methods; Metastability; Spectral methods; Homoclinic orbits; Exponential convergence; Hermite functions; Metastability; Spectral method; Numerical analysis; Approximate method; Differential equation; Applied mathematics; Homoclinic orbit; 34B15; 34C37; 41A30; 42C15; 65L10; 65T99; Fourier analysis
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2006.09.016

We present a spectral method for the computation of homoclinic orbits in ordinary differential equations. The method is based on Hermite–Fourier expansions of the complete homoclinic solution and exhibits exponential convergence. In addition, our method can be used to approximate nonlinear functionals which depend on the complete homoclinic solution. This is demonstrated using examples from phase separation dynamics and metastability.