Applied Mathematics and Mechanics

, Volume 39, Issue 11, pp 1547–1566 | Cite as

A simultaneous space-time wavelet method for nonlinear initial boundary value problems

  • Jizeng WangEmail author
  • Lei Zhang
  • Youhe Zhou


A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the Nth-order accuracy, as long as the Coiflet with [0, 3N − 1] compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method.

Key words

nonlinear initial boundary value problem Coiflet numerical method 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education, College of Civil Engineering and MechanicsLanzhou UniversityLanzhouChina

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