Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Adomian's decomposition method for eigenvalue problems.

Yee-Mou Kao1, T F Jiang

  • 1Institute of Applied Mathematics, National Chiao-Tung University, Hsinchu, Taiwan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

[New intraoral digital impression with pneumatic gingival retraction used in the restoration of crown for posterior teeth: a case report].

Zhonghua kou qiang yi xue za zhi = Zhonghua kouqiang yixue zazhi = Chinese journal of stomatology·2024
Same author

Photoelectric Properties of GaS<sub>1-</sub>Se<i></i> (0 ≤ <i>x</i> ≤ 1) Layered Crystals.

Nanomaterials (Basel, Switzerland)·2024
Same author

[A prospective cohort study to explore retention rate and behavior change among medium-to-low-tier female sex workers in Yuanzhou district, Yichun city].

Zhonghua yu fang yi xue za zhi [Chinese journal of preventive medicine]·2018
Same author

[Screening of hot-spot deafness gene mutations among 277 cochlear implantation patients in Sichuan province].

Lin chuang er bi yan hou tou jing wai ke za zhi = Journal of clinical otorhinolaryngology head and neck surgery·2018
Same author

Ehrenfest urn model with interaction.

Physical review. E·2018
Same author

Quantum fluctuations and stability of vortex lattices in a nonresonantly pumped exciton-polariton condensate.

Journal of physics. Condensed matter : an Institute of Physics journal·2017
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

This study extends Adomian's decomposition method for eigenvalue problems, introducing a Hamiltonian inverse iteration method for efficient ground state and excited state solutions. A space partition method enhances convergence for complex series expansions.

Area of Science:

  • Numerical Analysis
  • Computational Physics
  • Applied Mathematics

Background:

  • Adomian's decomposition method is effective for nonlinear boundary and initial value problems.
  • General eigenvalue problems require robust numerical techniques for accurate solutions.
  • Convergence issues can arise with standard series expansion methods.

Purpose of the Study:

  • To adapt Adomian's decomposition method for general eigenvalue problems.
  • To develop an efficient numerical method for finding eigenvalues and eigenfunctions.
  • To address convergence challenges in series expansion methods.

Main Methods:

  • Extension of Adomian's decomposition method.
  • Development of the Hamiltonian inverse iteration method.

Related Experiment Videos

  • Implementation of a space partition technique.

    • Main Results:

    • The Hamiltonian inverse iteration method rapidly provides ground state eigenvalues and eigenfunctions.
    • A method for determining excited states is successfully proposed.
    • The space partition method overcomes convergence failures in series expansions.

    Conclusions:

    • The extended Adomian's decomposition method offers a powerful approach for general eigenvalue problems.
    • The Hamiltonian inverse iteration method is efficient for both ground and excited states.
    • The space partition method significantly improves the applicability of series expansion techniques.