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Flexible exponential integration methods for large systems of differential equations

  • Dongping Li
  • Yuhao Cong
  • Kaifeng Xia
Original Research
  • 201 Downloads

Abstract

In this paper, we describe a flexible variant of exponential integration methods for large systems of differential equations. This version possesses the flexibility and generality which allows to further exploit the special structure of the system. By using modified B-series and bi-coloured rooted trees, we can derive the general structure of the classical order conditions for these schemes. Some numerical schemes are constructed and the order conditions are derived. Numerical experiments with reaction-diffusion type problems are included.

Keywords

Exponential integrators Rosenbrock methods Runge–Kutta methods Classical order conditions B-series 

Mathematics Subject Classification

65M12 65L06 65L20 

Notes

Acknowledgments

The authors gratefully acknowledge the supports of the National Science Foundation Grant (11471217) of China.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2015

Authors and Affiliations

  1. 1.Mathematics and Science CollegeShanghai Normal UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsChangchun Normal UniversityChangchunPeople’s Republic of China

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