一类含参数的正交多项式和一族新型R-K方法

A class of orthogonal polynomials with parameter and a family of new type R-K methods

提出一类于 [0 ,1]上关于权函数 ρ(δ ;t) =δ -t(δ≥ 1为参数 )正交的多项式 ,并利用这类正交多项式构造了一族新型s级 2s- 1阶R K方法 ,称之为δ RK方法 .当参数δ适当选择时 ,从这族方法中可以产生s个具有步长控制能力的新型R K方法 .

This paper presents a class of orthogonal polynomials on interval [0,1] with respect to the weight function ρ(δ;x)=δ-x in which δ ≥1 is a parameter,and a family of s stage (2s-1)st order new type Runge Kutta methods,which are named δ RK methods,constructed by the use of the class of orthogonal polynomials.When the parameter δ is chosen properly, s new type Runge Kutta methods with stepsize control capability can be obtained from the family of the δ RK methods.