Numerical solutions of nonstandard first order initial value problems (Q1186525)

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 right hand side local solution of the problem (*) is proved. Four numerical schemes linearly convergent to the solution of the problem (*) are presented. For all schemes convergence and error estimates are discussed. A numerical example for various stepsizes is solved using these schemes. The graphs of solutions are presented.