简介：The(2+1)-dimensionalBKPequationintheHirotabilinearformisstudiedduringthiswork.WronskianandGrammiantechniquesareappliedtotheconstructionofWronskianandGrammiansolutionsofthisequation,respectively.ItisshownthatthesesolutionscanbeexpressedasnotonlyPfaffiansbutalsoWronskiansandGrammians.

简介：AhighlyefficientH1-Galerkinmixedfiniteelementmethod(MFEM)ispresentedwithlineartriangularelementfortheparabolicintegro-differentialequation.Firstly,somenewresultsabouttheintegralestimationandasymptoticexpansionsarestudied.Then,thesuperconvergenceoforderO(h2)forboththeoriginalvariableuinH1(π)normandthefluxp=uinH(div,π)normisderivedthroughtheinterpolationpostprocessingtechnique.Furthermore,withthehelpoftheasymptoticexpansionsandasuitableauxiliaryproblem,theextrapolationsolutionswithaccuracyO(h3)areobtainedfortheabovetwovariables.Finally,somenumericalresultsareprovidedtoconfirmvalidityofthetheoreticalanalysisandexcellentperformanceoftheproposedmethod.