Discrete Petrov-Galerkin scheme for boundary value differential and integral problems: Theory and applications (Q2486773)

The paper deals with \(m^{th}\)-order ordinary differential and integrodifferential equations of the form \[ u^{(m)}(x) = (Fu)(x), \quad a<x<b, \] subject to \(m\) side conditions \[ G_j u = 0, \quad j=1,\dots,m, \] where \(F\) and \(G\) are given (nonlinear) maps defined on the space \(W_p^m(a,b)\), \(p \in [1,\infty]\). The authors analyse the error of the respective discrete Petrov-Galerkin scheme and prove optimal order convergence results. Various numerical experiments are presented.