Abstract
The Sturm-Liouville-Vodicka-Tittle procedure is extended to handle deterministic and nondeterministic nonconservative phenomena modelled by multiply connected nonself adjoint differential operators. This generalization is facilitated by employing the properties of adjoint differential operators to develop a piecewise weighted bi-orthogonality principle. Employing the inherent generality of the bi-orthogonality principle, an integral transform procedure is established which can handle multiply connected nonself adjoint differential operators subject to deterministic as well as homogeneous and nonhomogeneous nondeterministic initial, external and interdomain conditions. Due to the inherent scope of the procedure, in addition to the mean, both the variance and covariance of the governing field variables are obtained. Furthermore, generalizations to all the higher order statistical moments can be developed as required.
Published Version
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