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arXiv · 2508.06867

Efficient iterative linearised solvers for numerical approximations of stochastic Stefan problems

Muhammad Awais Khan·Jérôme Droniou·Kim-Ngan Le·Iuliu Sorin Pop
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Abstract

We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear equation associated with this scheme. We explore several approaches, from a standard Newton technique to linearised solvers. The latter offer the advantage of using the same coefficient matrix of the linearised system in each nonlinear iteration, for all time steps, and across all realisations of the Brownian motions. As a consequence, the system can be factorised once and for all. Although the linearised approach has a slower convergence rate, our sensitivity analysis and the use of adaptive tolerance in both deterministic and stochastic cases provide valuable insights for choosing the most effective solver across various scenarii.

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Muhammad Awais Khan, Jérôme Droniou, Kim-Ngan Le, Iuliu Sorin Pop. 2025-08-09. Efficient iterative linearised solvers for numerical approximations of stochastic Stefan problems. https://arxiv.org/abs/2508.06867

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