Convergence of numerical solution for the inhomogeneous Landau‐Lifshitz equations with Gilbert damping

Abstract

In this paper, we discuss the inhomogeneous Landau‐Lifshitz equation with nonuniform Gilbert damping term by numerical method. First, we establish a semi‐discrete form for the inhomogeneous Landau‐Lifshitz equation with nonuniform Gilbert damping, which is continuous in time. Then we study the temporal discretization. It proposes a simple projection method to solve our issue. Finally, we prove that it is unconditionally stable.