Exponential Multistep Methods for Stiff Delay Differential Equations

Stiff delay differential equations are frequently utilized in practice, but their numerical simulations difficult due to the complicated interaction between stiff and terms. At moment, only a few low-order algorithms offer acceptable convergent stable features. Exponential integrators type of efficient approach for problems that can eliminate influence stiffness on scheme by precisely dealing with term. This study is concerned two exponential multistep methods Adams equations. For semilinear equations, applying linear method directly integral form equation yields method. It shown proposed k-step stiffly order k. On other hand, we follow strategy Rosenbrock linearize along solution each step. The so-called constructed transformed equation. be easily extended nonlinear main contribution this show k+1 within framework strongly continuous semigroup Banach space. As result, developed may solve abstract served as time matching partial Numerical experiments presented demonstrate theoretical results.