【摘要】 采用谱Legendre-Galerkin方法求解第二类Volterra积分微分方程.当核函数k(x,s)=k(x-s)和源函数充分光滑且满足M-条件时,证明了问题的解u必定也满足M-条件.在此基础上,进一步证明了谱Legendre-Galer-kin方法求解第二类Volterra积分微分方程时在L2和L∞意义下的超几何收敛性.而且数值结果很好地反映了理论预期.更多还原

【Abstract】 Spectral Legendre-Galerkin apporach is applied for the second-kind Volterra integro-differential equations.When the kernel function k(x,s)=k(x-s) and the source function are smooth enough and satisfy the M-condition,the solution u has also been proved to satisfy the M-condition.Based on it,the supergeometric convergence of the spectral Legendre-Galerkin method for the second-kind Volterra integro-differential equation in L2 and L∞ norms is proved.Further the numerical results validate the theoretical prediction.更多还原