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The shooting techniques for the solution of two-point boundary value problems. (English)
MapleTech 3, No. 1, 85-93 (1996).
Summary: One of the strengths of Maple is its ability to provide a wide variety of information about differential equations. Explicit, implicit, parametric, series, Laplace transform, numerical, and graphical solutions can all be obtained via the ${\tt$dsolve} command. Numerical solutions are of particular interest due to the fact that exact solutions do not exist, in closed form, for most engineering and scientific applications. The numerical solution methods available within ${\tt$dsolve} are applicable only to ${\it$initial value problems}. Thus, at first glance, Maple appears to be very limited in its ability to analyze the multitude of two-point boudadry value problems that occur frequently in engineering analysis. $\medskip A$ commonly used numerical method for the solution of two-point boundary value problems is the ${\it$shooting method}. This well-known technique is an iterative algorithm which attempts to identify appropriate initial conditions for a related initial value problem (IVP) that provides the solution to the original boundary value problem (BVP). $\medskip$The first objective of the paper is to describe the shooting method and its Maple implementation ${\tt$shoot}. Then, ${\tt$shoot} is used to analyze three common two-point BVPs from chemical engineering: the Blasius solution for laminar boundary-layer flow past a flat plate, the reactivity behavior of porous catalyst particles subject to both internal mass concentration gradients and temperature gradients, and the steady-state flow near an infinite rotating disk.
Classification: I.1.4 I.1.3 G.1.7 G.4