A new approach to boundary value equations and application to a generalization of Airy's equation
For the boundary value problem: \(u''-kxu=g\), \(u(-1)=u(1)=0\), where k and g are constants, the authors compute a power series solution \(u=\Sigma_ nu_ n\) with the iteration \(u_ 0=c_ 1+c_ 2x+gx^ 2/2,\) \(u''_{n+1}=kxu_ n.\) A similar computation is carried out for the equation \(u''+au=g\) with general linear boundary conditions. The paper concludes stating a similar iteration for the equation \(u_{xx}+au_{yy}=g\) with linear boundary conditions and constant a, g.
scientific article; zbMATH DE number 4111934