The reproducing kernel algorithm for handling differential algebraic systems of ordinary differential equations (Q2830330)

This paper reports about the reproducing kernel Hilbert space method to solve the initial value problem for a system of differential-algebraic ordinary equations. This problem is presented, using the product of two Hilbert spaces, in the matrix form NEWLINE\[NEWLINE LU(t) = N(t,U(t)), \qquad t\in [a,b], \qquad U(a)=\alpha. NEWLINE\]NEWLINE An approximate solution is obtained as a truncated series, constructed by a system of orthogonal functions. The numerical results of this method are compared with the solutions obtained by other methods for three simple examples.