Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations

Shengrong Wu

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arXiv · 2609.08421

Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations

Shengrong Wu

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Abstract

We present an iteration algorithm for vacuum and Einstein scalar-field equations in double-null gauge, which transform the non-linear PDE into systems of ODE. The numerical realization combines characteristic constraint solves, LGL spectral elements, pole-free spherical operators, Galerkin projection, and independent first-order residual and consistency checks.

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Shengrong Wu. 2026-09-08. Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations. https://arxiv.org/abs/2609.08421

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