In this paper,we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries *** quadratic auxiliary variable approach is first proposed to...
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In this paper,we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries *** quadratic auxiliary variable approach is first proposed to reformulate the original model into an equivalent system,which transforms the energy conservation law of the Korteweg-de Vries equation into two quadratic invariants of the reformulated *** the symplectic Runge-Kutta methods are directly employed for the reformulated model to arrive at a new kind of time semi-discrete schemes for the original *** consistent initial conditions,the proposed methods are rigorously proved to maintain the original energy conservation law of the Korteweg-de Vries *** addition,the Fourier pseudo-spectral method is used for spatial discretization,resulting in fully discrete energy-preserving *** implement the proposed methods effectively,we present a very efficient iterative technique,which not only greatly saves the calculation cost,but also achieves the purpose of practically preserving *** numerical results are addressed to confirm the expected order of accuracy,conservative property and efficiency of the proposed algorithms.
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