Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 152, Issue -, Pages 143-154Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2023.10.013
Keywords
Geometric integration; Blow-up solutions; Non-linear partial differential equations; Nonlinear systems of equations; Splitting methods
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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.
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.
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