Boundary value problems in time-varying linear differential-algebraic equations: a standard canonical form approach to solvability
DOI:
https://doi.org/10.70474/w14jvq28Keywords:
Boundary value problem, time-varying linear differential-algebraic equation, standard canonical form, generalized inverseAbstract
This paper addresses the solvability of two-point boundary value problems for linear differential-algebraic equations with time-varying coefficients. The proposed method employs the standard canonical form to decouple the system into an ordinary differential part and an algebraic part. By introducing an appropriate parameter, we transform the original problem into the solvability of an associated linear algebraic system. This reduction leads to a constructive solvability criterion for the boundary value problem. A comprehensive example is provided to demonstrate the applicability and effectiveness of the proposed approach.
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