For a static singular beam equation and a static non-uniform beam equation under external static loads, we develop boundary functions method (BFM) and energy boundary functions method (EBFM) to find the deflection curves, which automatically satisfy the boundary conditions. Furthermore, the EBFM is also designed to preserve the energy. Both methods can quickly find accurate numerical solutions of static beam equations, and depict well the singular boundary layer behavior that appeared in the second-order differential term for the simply-supported and two-end fixed beams, and in the third-order differential term for the cantilever beam. Owing to the preservation of both the boundary conditions and energy, the EBFM is superior than the BFM, the shooting method, the weak-form method as well as the weak-form exponential trial functions method.

对于在外部静载荷下的静态奇异梁方程和静态非均匀梁方程，我们开发了边界函数方法（BFM）和能量边界函数方法（EBFM）来找到自动满足边界条件的挠度曲线。此外，EBFM还旨在保存能量。两种方法都可以快速找到静态梁方程的精确数值解，并很好地描述了在简支和两端固定梁的二阶微分项和三阶微分项中出现的奇异边界层行为。用于悬臂梁。由于保留了边界条件和能量，因此EBFM优于BFM，射击方法，弱形式方法以及弱形式指数试验函数方法。