On the Construction of Series Solutions to the First Biharmonic Boundary Value Problem on a Rectangle
Charles V. Coffman · SIAM Journal on Mathematical Analysis · 1986
This paper is concerned with the problem of finding a biharmonic function u on a rectangle $\Omega $ which vanishes on $\partial \Omega $ and has a preassigned normal derivative there. The solution u is developed in a series; however the family of functions that enters into this series development is not orthogonal and thus the determination of the coefficients requires the solution of an infinite system of linear equations. In implementation of this method of course the coefficients are obtained by solving a truncation of the original infinite system. The bulk of the paper is devoted to the estimation of the error that results from this truncation.