The Fokker–Planck equation derived by Brown for the probability density function of the orientation of the magnetic moment of single domain particles is one of the basic equations in the theory of superparamagnetism. Brown’s equation has an analytical solution, which is represented as a series in spherical harmonics with time-dependent coefficients. This analytical solution is commonly used when studying problems related to Brown’s equation. However, for particles with complex magnetic anisotropy, calculating the coefficients of the analytical solution can be a rather difficult task. In this paper, we propose an algorithm for the numerical solution of Brown’s equation based on the finite element method. The algorithm allows numerically solving Brown’s equation for particles with anisotropy of a fairly general form for constant and variable magnetic fields and with time-dependent temperature and other model parameters. In particular, an example of the numerical solution of an equation for particles with cubic anisotropy accounting two anisotropy constants and variable temperature is presented.

布朗针对单畴粒子磁矩取向的概率密度函数得出的Fokker-Planck方程是超顺磁性理论中的基本方程之一。布朗方程有一个解析解，用具有时间相关系数的一系列球谐函数表示。在研究与布朗方程有关的问题时，通常使用这种解析解。但是，对于具有复杂磁各向异性的粒子，计算分析溶液的系数可能是一项相当困难的任务。本文提出了一种基于有限元方法的布朗方程数值解算法。该算法可以对具有恒定磁场和可变磁场且时变温度和其他模型参数具有相当普遍形式的各向异性的粒子进行数值求解布朗方程。特别地，给出了具有立方各向异性的粒子的方程的数值解的示例，该立方各向异性考虑了两个各向异性常数和可变温度。