The differential transform method (DTM) is a simple technique based on the Taylor series. Applying the DTM, a given linear boundary eigenvalue problem (BEVP) involving ordinary differential equations is converted into a recurrence relation or a system of recurrence relations for the Taylor coefficients. This ultimately leads to the solution of the problem in the form of an infinite power series with an appropriate region of convergence. The present paper aims to apply the DTM in solving a BEVP arising from the Darcy–Brinkman convection in a rectangular box subject to general boundary conditions whose vertical sidewalls are assumed to be impermeable and adiabatic. The non‐dimensional temperature difference between the plates represented by the Darcy–Rayleigh number, the eigenvalue of the problem, is obtained as a function of the width of the Bénard cell ( $\frac{2\pi }{b}$ : b is the horizontal wave number) and other parameters using the DTM. The work includes investigation on the convergence of the series solution. The solution by the DTM is compared with that obtained by the MATLAB bvp4c routine and excellent agreement is found thereby establishing the accuracy of the DTM.

中文翻译：

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关于求解边界特征值问题的微分变换方法：一个例子

差分变换方法（DTM）是基于泰勒级数的简单技术。应用DTM，将涉及常微分方程的给定线性边界特征值问题（BEVP）转换为泰勒系数的递归关系或递归关系系统。最终以具有适当收敛区域的无限幂级数的形式解决了问题。本文旨在将DTM应用于求解矩形箱中达西-布林克曼对流引起的BEVP，该矩形箱在一般边界条件下被假定，其垂直侧壁被假定为不可渗透且绝热的。平板之间的无量纲温差由Darcy-Rayleigh数表示，即问题的特征值，$\frac{\mathrm{2个}\pi }{b}$：b是水平波数）和使用DTM的其他参数。这项工作包括调查级数解的收敛性。将DTM的解决方案与MATLAB bvp4c例程所获得的解决方案进行比较，发现极好的一致性，从而建立了DTM的准确性。