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September 10, 2025MathematicsOpen Access

Theory of Functional Connections Applied to Linear Discontinuous Differential Equations

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Two methods address discontinuities in linear differential equations, demonstrating accuracy through validation.

Proposed methods achieve high accuracy, with errors approaching machine precision in complex equations.
Validation includes both second-order initial value and boundary value problems to test method effectiveness.
The first method incorporates discontinuities directly, while the second uses piecewise constrained expressions.
Applications demonstrate successful resolution of third-order differential equations with known analytical solutions.

White et al. (2025) studied this question.

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