A collocation method for eigenvalue problems

Approximations to the eigenvalues ofmth-order linear eigenvalue problems are determined by using a collocation method with piecewise-polynomial functions of degreem+d possessingm continuous derivatives as basis functions. It is shown that for a general class of problems the error in these approximations is at leastO([h(II)] ^d+1) whereh(II) is the maximal subinterval length. The question of stability of the discretized problems is also considered. It is not assumed that the eigenvalue problems are in any sense self-adjoint.