An implicit two-point numerical integration formula for linear and nonlinear stiff systems of ordinary differential equations

Abstract

In [1], the author proposed a semi-implicit one-step integration formula which effectively copes with linear systems of ordinary differential equations with widely varying eigenvalues. The integration algorithm is based on a local representation of the theoretical solution to the initial value problem by a linear combination of exponential functions. The resultant integration formula is of order four. Unfortunately, this algorithm cannot cope with nonlinear stiff systems of ordinary differential equations. In this paper, the author extends the concept adopted in [1] to construct an implicit two-point formula which can effectively cope with nonlinear stiff systems. The resultant integration formula is of order five and it is L-stable and convergent.