The adapted block boundary value methods for singular initial value problems

This paper deals with the numerical methods for solving singular initial value problems. By adapting the block boundary value methods (BBVMs) for regular initial value problems, a class of adapted BBVMs are constructed for singular initial value problems. It is proved under some suitable conditions that the adapted BBVMs are uniquely solvable, stable and convergent of order p, where p is the consistence order of the methods. Several numerical examples are performed to verify the stability, efficiency and accuracy of the adapted methods. Moreover, a comparison between the adapted BBVMs and the IEM-based iterated defect correction methods is given. The numerical results show that the adapted BBVMs are comparable.