... , c = c 0 + c 1 T , E = E 0 + E 1 T , β = β 0 + β 1 T Most of the problems arising in science and engineering are governed by nonlinear differential equations. There are several methods for solving these equations including perturbation...

... nonlinear differential equations Runge-Kutta methods slip flow subsonic flow leak flow rate friction factor narrow crack Estimation of leak flow rates is increasing in importance for a variety of industries that use a leak-before-break (LBB) safety assessment as a method of nondestructive...

... while ϱ t designates the pipe density. pipes partial differential equations nonlinear differential equations Metallic piping systems conveying liquids may be subjected to inelastic pipe wall deformations when fluid transients are generated ( 1 2 ). Depending on pressure surges...

... received by the PVP Division November 17, 2002; revision received June 4, 2003. Associate Editor: R. J. Scavuzzo. 17 November 2002 04 June 2003 04 11 2003 steel bending stress-strain relations nonlinear differential equations failure (mechanical) buckling...