Applications of modified Mickens-type NSFD schemes to Lane–Emden equations

If there is a jump discontinuity present in the forcing term of a boundary value problem (BVP), the nonstandard finite difference (NSFD) and finite difference (FD) methods do not approximate the solutions very well. Here we use fuzzy transforms (FTs) and derive fuzzy transformed NSFD schemes that are referred to as non-standard fuzzy transform methods (NFTMs). The convergence of the derived NFTMs is established. Numerical solutions of Lane–Emden type equations are obtained using NFTMs. We show that NFTMs provide better results than NSFD and FD methods when the forcing term has a jump discontinuity. Even for large jumps, the NFTMs provide more accurate results than the other methods.