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We consider the boundary value problems (BVPs) for linear secondorder ODEswith a strongly positive operator coefficient in a Banach space. The solutionsare given in the form of the infinite series by means of the Cayley transformof the operator, the Meixner type polynomials of the independent variable, theoperator Green function and the Fourier series representation for theright-hand side of the equation. The approximate solution of each problem is apartial sum of N (or expressed through N) summands. We prove the weighted errorestimates depending on the discretization parameter N, the distance of theindependent variable to the boundary points of the interval and some smoothnessproperties of the input data.

Weighted estimates of the Cayley transform method for boundary value problems in a Banach space