The various order explicit multistep exponential fitting for systems of ordinary differential equations

We develop various order-explicit multistep schemes of exponential fitting for systems of ordinary differential equations. The schemes may be applied to systems whose linear part is nondiagonal. Various precisions can be achieved by employing the various order schemes. Comparisons of accuracy and efficiency of numerical solutions are mentioned in the examples. The numerical results show that the schemes are highly accurate and computationally efficient.