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We report on a novel algorithm for controlling global error in a step-by-step(stepwise) sense, in the numerical solution of a scalar, autonomous, nonstiffor weakly stiff problem. The algorithm exploits the remainder term of a Taylorexpansion of the solution. It requires the use of the DP853 triple to solve anauxiliary problem which, in turn, enables the remainder term to be determined.A quenching process then allows the solution generated by Euler's method to becontrolled. We have achieved tolerances on the relative global error as strictas 1e-10.

Stepwise global error control in Euler's method using the DP853 triple and the Taylor remainder term