An asymptotic preserving semi-implicit multiderivative solver

In this work we construct a multiderivative implicit-explicit (IMEX) scheme for class of stiff ordinary differential equations (ODEs). Our solver is high-order accurate and has an asymptotic preserving (AP) property large singularly perturbed ODEs. context, the AP means that singular limit discretely preserved when parameter ? goes to zero. The proposed method based upon two-derivative backward Taylor series base solver, which show property. Higher order accuracies are found by iterating result over interpolant right hand side function, again prove Theoretical results showcasing consistency as well accuracy presented. addition, extension arbitrarily split function also offered. Numerical collection standard test cases from literature presented support theoretical findings paper.