Flexible exponential integration methods for large systems of differential equations
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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.
KeywordsExponential integrators Rosenbrock methods Runge–Kutta methods Classical order conditions B-series
Mathematics Subject Classification65M12 65L06 65L20
The authors gratefully acknowledge the supports of the National Science Foundation Grant (11471217) of China.
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