Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations
For the vector difference equation \(\Delta^2 y_{k+1}= f(x_k,y_k, \Delta y_k)\), \(k=1,\dots, n-1\), \(\Delta y_k= (y_k-y_{k-1})/h\), with nonlinear boundary conditions at \(k=0\) and \(k=n\), the existence of the solution and its convergence as \(h\to 0\), \(x_k=k h\to x\) are investigated.
scientific article; zbMATH DE number 1794943