Spurious fixed points of a variable step size, variable order, predictor corrector algorithm Original Research Article

This work presents a rigorous analysis of the potential for spurious fixed points of a widely used adaptive predictor corrector algorithm of Shampine and Gordon. On the negative side, we show how to construct differential equations on which spurious fixed points may arise. However, on the positive side, we prove that any spurious fixed point has a residual that is of the order of the error tolerance.