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arXiv · 2608.30062

An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions

So-Hsiang Chou·Patrick Nyadjo Fonga
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Abstract

We develop an immersed interface finite difference method for a one-dimensional nonlinear parabolic interface problem with jump condition \[ [u]_α=λu^+u^-. \] The method combines a Crank--Nicolson immersed interface discretization with an \(s\)-parameter reduction of the nonlinear interface condition, thereby reducing the nonlinear coupling to a scalar quadratic equation. We also discuss two different viewpoints for combining Newton iteration with immersed interface discretization, namely the IIM--Newton and Newton--IIM formulations. Numerical experiments are presented to illustrate the behavior and accuracy of the method.

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So-Hsiang Chou, Patrick Nyadjo Fonga. 2026-08-30. An Immersed Interface Method for Parabolic Interface Problems with Nonlinear Jump Conditions. https://arxiv.org/abs/2608.30062

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