On solving systems of differential algebraic equations (Q1207977)

A system of differential algebraic equations \(x'=f(t,x,y)\), \(y=g(t,x,y)\), \(x(0)=0\) is studied under the validity of many assumptions, e.g. \(f\), \(g\) fulfill local Lipschitz conditions. The convergence of successive approximations \(x_{k+1}(t)=\int_ 0^ t f(s,x_ k(s),y_ k(s))ds\), \(y_{k+1}=g(t,\bar x,\bar y))\), \(x_ 0\), \(y_ 0\) arbitrary, is proved where either \(\bar x=x_ k(t)\), \(\bar y=y_ k(t)\) (Picard method) or \(\bar x=x_{k+1}(t)\), \(\bar y=y_ k(t)\) (Seidel method).