Solving Singular Differential-Algebraic System Subject to Nonlocal Integral Boundary Conditions Using Generalized Inverse
DOI:
https://doi.org/10.65405/7zd8wq14Keywords:
Singular differential systems, generalized inverse, integral boundary conditions, Fundamental matrix, Characteristic operatorAbstract
This paper investigates a novel class of first-order linear singular differential-algebraic systems subject to generalized multi-point nonlocal integral boundary conditions. By systematically utilizing the Moore-Penrose generalized inverse and orthogonal operators, the intractable singular system is decoupled and regularized into an equivalent tractable ordinary differential system. Furthermore, by incorporating distributed integral constraints over the entire domain, we derive a modified generalized algebraic shooting matrix. Rigorous existence and uniqueness criteria for the solution are established under standard tractability assumptions. Finally, an illustrative numerical example is provided to demonstrate the practical validity and efficiency of the proposed analytical framework.
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