一类广义Burgers－BBM方程的Fourier谱方法及误差估计

THE SPECTRAL METHOD AND ERROR ESTIMATION FOR A CLASS OF GENERALIZED BURGERS-BBM EQUATIONS

本文对［３－５］中提出的一类广义的Ｂｕｒｇｅｒｓ－ＢＢＭ方程的周期初值问题建立了不同于［５］的谱方法。构造了半离散和全离散的Ｆｏｕｒｉｅｒ－Ｇａｌｅｒｋｉｎ格式，从理论上给出了半离散和全离散格式近似解的收敛性证明及严格的误差估计。改进了［５］的结果。

In this paper,Fourier spectral methods of Galerkin for a class of generalized Burgers-BBM equations are presented.The semidiscrete and fully discrete schemes are comstructed,and the error estimate of semidiscrete and fully discrete approximation solutions is given。