Second‐order modified positive and elementary stable nonstandard numerical methods for n$$ n $$‐dimensional autonomous differential equations

Abstract

A novel technique is presented to construct and analyze second‐order modified positive and elementary stable nonstandard (SOPESN) numerical methods for solving two general classes of ‐dimensional autonomous ordinary differential equations. The new SOPESN methods are second‐order generalizations of the explicit Euler's method, thereby improving the order of accuracy of the underlying numerical method. Numerical simulations are presented to validate the theoretical results and highlight the advantages of the proposed new modified nonstandard methods over existing standard and nonstandard numerical methods.