中文摘要：

对二维半无界条状区域上的四阶偏微分方程,用不带权函数的Laguerre-Legendre混合谱方法进行逼近.通过构造满足微分方程边界条件的基函数,由离散变分公式可以得到具有稀疏系数矩阵的代数系统,从而有效地进行求解.对该方法进行严格的收敛性分析,数值结果验证了方法的收敛性和有效性.

英文摘要：

Mixed Laguerre-Legendre spectral method without weight function is presented to solve the fourth-order equations in a semi-infinite channel.By constructing appropriate basis functions satisfying the boundary conditions,the coefficient matrix of the corresponding linear system is sparse,and the solution can be solved efficiently.Rigorous analysis of the convergence of this method is carried out.Numerical experiments are given to confirm the convergence and efficiency of the method.