The molecule solution of an extended discrete LotkaVolterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is shown that our new sequence transformation accelerates some kinds of linearly convergent sequences and factorially convergent sequences with good numerical stability. Some numerical examples are also presented.

The minimal speeds (c) of the KolmogorovPetrovskyPiskunov (KPP) fronts at small diffusion ( 1) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle of c reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advectiondiffusion operator with spacetime periodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In contrast to the scaling c= O ( 1/4) in steady cellular flows, a new relation c= O (1) as 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub

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We prove that the algebraicmultiplicity of a holomorphic vector field at an isolated singularity is invariant by topological equivalences which are differentiable at the singular point.

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