Constructive Approaches for Analyzing Partial Linear Differential Operators on Finite Intervals: A Comprehensive Study

DOI: https://doie.org/10.1213/Jbse.2024156581

Avinash Bansidhar Thakare, Dr Sadanand Patil

Keywords:

Constructive analysis, partial linear differential operators, finite intervals, boundary value problems, approximation methods, stability, mathematical physics.

Abstract:

This article presents a constructive analysis of partial linear differential operators (PL- DOs) on finite intervals, with a focus on solution existence, uniqueness, and stability. The theoretical framework builds on fundamental aspects of functional analysis and opera- tor theory. By employing constructive techniques, we develop a systematic approach to address boundary value problems associated with PLDOs, facilitating applications in mathematical physics, engineering, and other fields. The analysis reveals significant in- sights into operator behavior in finite domains, offering novel contributions to the existing body of knowledge

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