Abstract
The purpose of this paper is to investigate the solution of the fourth order boundary value problem with boundary conditions where α(s) is square integrable on 0≦s≦a, bounded from above by M and below by M >0 and 0≦z≦∞. This problem arises in certain areas of fluid dynamics. If [0, a] is divided into equal intervals of length h such that and ū is a vector with ith component u(si,z) the asssociated vector differential equation is . The eigenvalues of AB are shown to be nonnegative and the matrix of eigenveciors to have bounded condition number, which assures that the solution remains bounded as h→0, and hence the solution of the boundary value problem exists.
†The Institute for Computer Applications in Science and Engineering is sponsored by NASA grant NGR 47-102-001.
†The Institute for Computer Applications in Science and Engineering is sponsored by NASA grant NGR 47-102-001.
Notes
†The Institute for Computer Applications in Science and Engineering is sponsored by NASA grant NGR 47-102-001.