B-methods for the numerical solution of evolution problems with blow-up solutions part II: Splitting methods

B-methods are numerical methods which are especially tailored to solve non-linear partial differential equation that have blow up solutions. We have presented in Part I a systematic construction of B-methods based on the variation of constants formula. Here, we use splitting methods as a second way to construct B-methods, and we prove several special properties of such methods. We illustrate our analysis with numerical experiments.

Automated summary

This article introduces a special numerical method called B-method for solving blow up solutions in non-linear partial differential equations. The authors construct B-methods using the variation of constants formula and splitting methods, and prove several special properties of these methods.