Runge-Kutta方法用于非线性方程求根

将Runge-Kutta方法用于非线性方程求根问题,给出二阶,三阶和四阶对应的三个新的方程求根公式,证明了它们至少三次收敛到单根,线性收敛到重根.文末给出数值试验,且与其它已知求根公式做了比较.结果表明此方法具有较好的优越性,它们丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值.

Runge-Kutta Methods Application in Solving Foots of Nonliner Equation

Runge-Kutta methods are used to solve the roots of nonliner equation.Three new solving root schemes are gived which are of second order,third order and fourth order of Runge-Kutta methods.Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known variant Newton′s methods.The results show that the proposed methods have some more advantages than the others.They enrich the methods to find the roots of non-linear equation and have great importance in both theory and application.