一般形式的奇异对偶积分方程组正交多项式求解法

Orthogonal Polynomial Solving Method of General Singular Dual Integral Equations

基于Jacobi正交多项式法,直接求解一般形式的对偶积分方程组,将对偶积分方程组中的未知函数,表示成n次Jacobi正交多项式级数,用正交多项式将奇异对偶积分方程组,化成线性代数方程组,通过求解级数中的各项系数,由此给出奇异对偶积分方程组的一般性解,并严格证明了奇异对偶积分方程组和由它化成的线性代数方程组的等价性,解的存在性和解的表示形式不唯一性．本文给出的理论解和解法,可供求解复杂的数学、物理、软科学中的混合边值问题应用．

Based on the method of Jacobi orthogonal polynome, general singular dual integral equations are expressed as the series of Jacobi orthogonal polynome on n order. The general singular dual integral equations are changed into linear algebraic equations by Jacobi orthogonal polynome. Thus general solutions are given through solving unknown coefficient of every term in the series. The eqnivalence between singular dual integral equations and by it changed into algebraic equations, existence and non-uniqueness of expressive form on the solutions are proved exactly. In this paper the given theoretical solutions and solving method provides application to problems of solving mixed boundary value of complex mathematics, physics, soft science.