Sixth-order, P-stable, Numerov-type methods for use at moderate accuracies

We consider a family of half-implicit Numerov-type methods for the numerical solution of the problem y('') = f(x, y). These methods use off-step points and waste four function evaluations (stages) per step. They attain sixth algebraic orders, while other methods of this type need five function evaluations per step. After we exploit this reduction in stages we construct a particular method and present various numerical tests on stiff periodic problems that justify its efficiency.

Automated summary

We explore a family of half-implicit Numerov-type methods for solving numerical problems, which achieve sixth algebraic orders and require four function evaluations per step. By reducing the number of stages, we develop a specific method and conduct numerical tests on stiff periodic problems to demonstrate its efficiency.