Quadratically convergent numerical schemes for nonstandard initial value problems (Q1184810)

The nonstandard initial value problem (*) \(y'(t)=f(t,y(t),y'(t))\), \(y(t_ 0)=y_ 0\) is considered. Under some assumptions on the function \(f\) the existence and uniqueness of the both sides local solution of the problem (*) is proved. A numerical scheme quadratically convergent to the solution of the problem (*) is presented. Convergence and error estimate of this schemes are discussed. The results of the paper are applied to two physical problems.