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

38. Valeriy R. Korostyshevskiy, Thomas Wanner:
    A Hermite spectral method for the computation of homoclinic orbits and associated functionals
    Journal of Computational and Applied Mathematics 206(2), pp. 986-1006, 2007.

Abstract

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.

Links

The published version of the paper can be found at https://doi.org/10.1016/j.cam.2006.09.016.

Bibtex

@article{korost:wanner:07a,
   author = {Valeriy R. Korostyshevskiy and Thomas Wanner},
   title = {A Hermite spectral method for the computation of homoclinic
            orbits and associated functionals},
   journal = {Journal of Computational and Applied Mathematics},
   year = 2007,
   volume = 206,
   number = 2,
   pages = {986--1006},
   doi = {10.1016/j.cam.2006.09.016}
   }