Iterative solution of nonlinear boundary-value problems (Q806982)

Third order nonlinear boundary value problems of the form \(y'''=f(x,y,y',y'')\), \(y(a)=A_ 1\), \(y'(b)=A_ 2\), \(y''(a)=A_ 3\) are considered. The function f is assumed to be continuous and Lipschitz continuous in the last three variables. An iterative scheme for y, \(y'\), \(y''\) motivated by Taylor's formula with integral remainders is considered and the integrals are approximated via the trapezoid rule. A convergence theory is given and four numerical examples are presented. The paper concludes with an appendix containing a code for the method.