A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind

Date

2022-01-01

Author

Kaya, Ruşen
Taşeli, Hasan

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A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are compared with the very well known eigenvalues of the Schrödinger equation with several types of potential functions v(x). It is shown that the eigenvalues recorded to about 15 significant figures are in excellent agreement with the results that exist in the literature.

Subject Keywords

Integral equation, Neumann boundary value problem, Rayleigh–Ritz method Dirichlet boundary value problem, Schrödinger equation

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85128815222&origin=inward
https://hdl.handle.net/11511/97113

Journal

Journal of Mathematical Chemistry

DOI

https://doi.org/10.1007/s10910-022-01344-9

Collections

Department of Mathematics, Article

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Citation Formats

R. Kaya and H. Taşeli, “A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind,” Journal of Mathematical Chemistry, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85128815222&origin=inward.