EIGEN FUNCTION EXPANSIONS ASSOCIATED WITH THE SECOND ORDER DIFFERENTIAL EQUATIONS

Mukesh Rani alias Mukta; Dr. Pooja Bhatia

EIGEN FUNCTION EXPANSIONS ASSOCIATED WITH THE SECOND ORDER DIFFERENTIAL EQUATIONS

Authors: Mukesh Rani alias Mukta, Dr. Pooja Bhatia

Unique Paper ID: 179109
Volume: 11
Issue: 12
PageNo: 6848-6852

Keywords: No Keywords Found

Abstract:
Eigenfunction expansions offer a key method for addressing second-order differential equations, particularly in boundary value problems and spectral analysis. This paper examines the theoretical basis, characteristics, and applications of eigenfunction expansions, illustrating how differential equations can be represented as an infinite series of orthogonal eigenfunctions. The analysis is based on Sturm-Liouville theory, wherein self-adjoint differential operators produce discrete eigenvalues and a complete set of orthogonal eigenfunctions. The expansion theorem asserts that any function in a specified space may be expressed as a summation of eigenfunctions, each multiplied by suitable coefficients. These expansions enable efficient solutions in quantum physics, fluid dynamics, wave propagation, and heat conduction through orthogonality and completeness. Moreover, boundary conditions are essential in determining eigenfunction behavior, affecting solution convergence and precision. This paper improves the mathematical tools for addressing physical and engineering problems by showing the existence, uniqueness, and asymptotic behavior of eigenfunction expansions. Future prospects emphasize the enhancement of computational methodologies for managing intricate systems and the expansion of eigenfunction applications in non-linear differential equations.

Download article

email to a friend

Cite This Article

ISSN: 2349-6002
Volume: 11
Issue: 12
PageNo: 6848-6852

EIGEN FUNCTION EXPANSIONS ASSOCIATED WITH THE SECOND ORDER DIFFERENTIAL EQUATIONS

Available:https://ijirt.org/Article?manuscript=179109

15 May, 2025

RISK-BASED SECURITY FRAMEWORKS FOR VANETS: A SYSTEMATIC REVIEW

08 May, 2025

A REVIEW ON CONDITION OF FEMALE WORKERS IN TEXTILE INDUSTRIES IN HARYANA

08 May, 2025

POSE FIT TRACKER WITH GYM MANAGEMENT SYSTEM

Impact Factor
8.01 (Year 2024)

UGC Approved
Journal no 47859

Join Our IPN

IJIRT Partner Network

Submit your research paper and those of your network (friends, colleagues, or peers) through your IPN account, and receive 800 INR for each paper that gets published.

Join Now

Latest Publication

Recent Conferences

NCSEM 2024

National Conference on Sustainable Engineering and Management - 2024 Last Date: 15th March 2024

Submit inquiry