Implicit-explicit one-leg methods for nonlinear stiff neutral equations

In this paper, by adapting the underlying implicit-explicit (IMEX) one-leg methods (cf. [1, 2]), a class of extended IMEX one-leg (EIEOL) methods are suggested for solving nonlinear stiff neutral equations (SNEs). It is proven under some suitable conditions that EIEOL methods are D-convergent of order 2 and stable for nonlinear SNEs. Several numerical examples are given to testify the obtained theoretical results and the computational effectiveness of EIEOL methods. Moreover, a comparison with the fully implicit one-leg methods is presented, which shows that EIEOL methods have the higher computational efficiency.