Abstract: This paper takes Legendra polynomials as the trial functions in the weighted residual method, so as to establish: 1. the least-square method, 2. the dispersion type least-square method, 3.Galerkin method, 4.the dispersion type Galerkin method. Due to the fact that there are orthogonal characteristic, odd-even characteristic, recursive characteristic, etc., the outlook of the application of this method is very bright.

摘要： 本文以勒让德多项式(Legendre)作为加权残数法中的试函数。建立1.最小二乘法,2.离散型最小二乘法,3.伽辽金法,4.离散型伽辽金法。由于勒让德多项式具有正交性质、奇偶性质、递推性质等,因此在固体力学中应用,前景美好。