... . The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement...

... transforms Fourier transforms initial value problems Fredholm integral equations In describing crack growth for brittle materials with cracks, in addition to well-known stress intensity factors (SIFs), elastic T -stress at a crack tip is also a significant fracture parameter ( 1 ). The so...

... (mechanical) initial value problems integral equations screw dislocations dislocation density Laplace transforms crack-edge stress field analysis 12 06 2005 26 09 2005 2006 American Society of Mechanical Engineers ...

..., i.e., r = a . Thus, in the conditional initial value problem approach, the unknowns u ′ r = 0 , w r = 0 , w ″ r = 0 are to be so determined as to result in a constrained dynamical trajectory which satisfies the boundary conditions...

... a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. A decrease in the cylinder radius will induce a stronger lateral capillary force and thus...

... Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 03 February 2000 15 August 2000 wave propagation fluctuations inhomogeneous media initial value...