An Explicit L-Stable Formula for Solving Stiff Problems

A L-stable formula is proposed for solving stiff problems. This formula can be classified as an explicit, one-step method. In general, it can have A-stability and L-stability in addition to first order accuracy. It is characterized by problem dependency since it has problem-dependent coefficients in the formulation. In general, it has the same properties as those of the backward Euler method, such as A-stability, L-stability and first order accuracy. However, the most important different property is that it is explicit while the backward Euler method is implicit. Hence, it will involve no nonlinear iterations in the solution of nonlinear stiff problems while an implicit method must be iteratively implemented for each step. Consequently, it is very computationally efficient in the solution of stiff problems when compared to the backward Euler method.