PreprintCC BY 4.0arXiv
Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations
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.
Related
- The Characteristic Initial Value Problem for the 3D Compressible Euler Equations
- Global large solutions of the Cauchy problem for the NS-NPP equations with Fujita-Kato type initial data
- Policy iteration for Hamilton-Jacobi-Isaacs equations with control constraints and comparison with Hamilton-Jacobi-Bellman equations
- The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton-Jacobi-Bellman Equations
- Flux-Matched Poisson Iteration for Generated Jacobian Equations: Local Convergence and Spectral Galerkin Approximation
BibTeX
@misc{wu2026picard,
title = {{Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations}},
author = {Shengrong Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08421},
eprint = {2609.08421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08421},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Picard Iteration for the Characteristic Initial Value Problem in Einstein Equations
AU - Shengrong Wu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08421
UR - https://arxiv.org/abs/2609.08421
AB - 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.
ER -