A HYBRID SPECTRAL DEFERRED CORRECTION METHOD WITH PHYSICS-INFORMED NEURAL NETWORK INITIALIZATION: A HYBRID SPECTRAL DEFERRED CORRECTION METHOD WITH PHYSICS-INFORMED NEURAL NETWORK INITIALIZATION

Ikrom Akramov; Tulqin Rasulov; Dilnora Kurbonova

doi:10.52754/16948645_2026_1(8)_39

Authors

Ikrom Akramov Bukhara state university
Tulqin Rasulov Bukhara state university
Dilnora Kurbonova Bukhara state university

DOI:

https://doi.org/10.52754/16948645_2026_1(8)_39

Keywords:

Spectral Deferred Correction (SDC), collocation problem, Physics-Informed Neural Network (PINN), initial guess.

Abstract

Spectral Deferred Correction (SDC) methods are iterative methods used to solve ordinary differential equations. The SDC method can achieve high-order convergence by adjusting the initial guess, quadrature nodes, and the number of iterations. Therefore, its convergence strongly depends on the initial approximation. In this work, we introduce a hybrid method in which a Physics-Informed Neural Network (PINN) provides the initial guess for SDC iterations. We present a rigorous formulation of both SDC and PINN, along with a convergence analysis of the proposed method. Finally, we validate our results using numerical examples. The proposed method significantly reduces the number of SDC sweeps required to achieve high-order accuracy.

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A HYBRID SPECTRAL DEFERRED CORRECTION METHOD WITH PHYSICS-INFORMED NEURAL NETWORK INITIALIZATION