2025/08/09 by Muhammad Awais Khan, Khan, Muhammad Awais, Jérôme Droniou +5
Computer Science · Economics, Econometrics and Finance · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Stochastic Gradient Optimization Techniques #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2508.06867
openalex publication_date 2025/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.