A fourth order extrapolation for the trapezoidal rule (Q1282127)

Denote by \(\{ y_n \}\) the numerical solution of a stiff differential equation obtained by the trapezoidal rule. In order to improve the accuracy of this approximation, the authors propose to add a correction term which can be computed by a linear recurrence relation that depends on \(\{ y_n \}\) and on the Jacobian of the problem. A linear stability analysis shows that the new approximation retains the A-stability. Numerical experiments are included which confirm the stability and the higher order of the new algorithm.