Third-order linearly implicitl-stable methods for stiff differential equations

This paper develops general criteria for third-order L-stable methods which require not more than three function evaluations and not more than four matrix-by-vector multiplications per step. The methods are required to remain third-order and provide a valid error estimate if the Jacobian matrix is replaced by an approximation with error of order h. Five specific types of methods are identified, and examples given of each type.