A class of orthogonal polynomials with parameter and a family of new type R-K methods
Shuang Zhao · Journal of Ningxia University · 2000
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.