Backward Euler method
（重定向自Implicit Euler method）
![The pink region outside the disk shows the stability region of the backward Euler method.](/Images/godic/202502/09/Stability_region_for_BDF1.svg2927.png")
In numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary differential equations. It is similar to the (standard) Euler method, but differs in that it is an implicit method. The backward Euler method has order one and is A-stable.