# Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach

## TL;DR

This paper develops a semi-discretized numerical method with exponential splitting for solving complex degenerate stochastic Kawarada equations, ensuring stability and key solution features on adaptive grids.

## Contribution

It introduces a novel semi-discretized approach combined with exponential splitting for degenerate stochastic PDEs, preserving positivity and stability.

## Key findings

- Key solution features are preserved under modest restrictions.
- The splitting method maintains stability without extra restrictions.
- Numerical experiments demonstrate convergence and effectiveness.

## Abstract

The numerical solution of a highly nonlinear two-dimensional degenerate stochastic Kawarada equation is investigated. A semi-discretized approximation in space is comprised on arbitrary nonuniform grids. Exponential splitting strategies are then applied to advance solutions of the semi-discretized scheme over adaptive grids in time. It is shown that key quenching solution features including the positivity and monotonicity are well preserved under modest restrictions. The numerical stability of the underlying splitting method is also maintained without any additional restriction. Computational experiments are provided to not only illustrate our results, but also provide further insights into the global nonlinear convergence of the numerical solution.