Second-order nonstandard explicit Euler method

Nonstandard finite difference (NSFD) methods provide an efficient way to numerically solve many problems in engineering and science. NSFD methods also provide many advantages over classical techniques, such as preserving important physical properties of the corresponding problem. In recent years, some NSFD methods were constructed that are elementary stable but only first order accurate. In this work, we propose and analyze a new non-standard finite difference method which is both elementary stable and of second order accuracy. In addition, we validate the new method using a set of numerical simulations.