Additive parameters methods for the numerical integration of \(y''=f(t,y,y')\)
The authors derive a new two step fourth-order method for the numerical integration of the general second-order differential equation \(y''(t)=f(t,y,y')\) subject to the initial conditions \(y(t_0)=y_0\), \(y'(t_0)=y_0'\). The method depends upon the parameters \(p\) and \(q\) which are the new additional values of the coefficients of \(y'\) and \(y\) in the given differential equation. Truncation error and order of the method are reported. It is shown that the method is absolute stable when the parameters are chosen as the coefficients of \(y'\) and \(y\) in the case of a linear differential equation. Numerical results are presented for Bessel's, Legendre's and general second-order differential equations.
scientific article; zbMATH DE number 908373