Trees, B-series and exponential integrators

Questions concerning the accuracy of numerical methods for differential equations are often analysed using B-series and other formulations based on rooted trees. The analysis of numerical methods, such as Rosenbrock and certain exponential methods, requires an additional algebraic structure to represent the direct use of Jacobian matrices in the computation. It is shown how this can be done within a context containing a broad review of the existing B-series formulation.

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Original source : http://imajna.oxfordjournals.org/cgi/content/short...