A method to find approximate solutions of first-order systems of nonlinear ordinary equations

We develop a one-step matrix method in order to obtain approximate solutions of first-order nonlinear systems and nonlinear ordinary differential equations, reducible to first-order systems. We find a sequence of such solutions that converge to the exact solution. We apply the method to different well-known examples and check its precision, in terms of local error, comparing it with the error produced by other methods. The advantage of the method over others widely used lies on the great simplicity of its implementation.

Automated summary

The one-step matrix method developed aims to obtain approximate solutions for first-order nonlinear systems and nonlinear ordinary differential equations reducible to first-order systems. The method is shown to converge to the exact solution with high precision, and its advantage over other commonly used methods lies in its simplicity of implementation.