Na T.Y. Computational Methods in Engineering Boundary Value Problems

Academic Press, 1980. - 346 Pages.Two-point boundary value problems occur in all branches of engineering and science. In these problems the boundary conditions are specified at two points. To complicate the matter, the governing differential equations for a majority of such problems are nonlinear; since analytic solutions do not in general exist, solutions have to be obtained by numerical methods. Methods for the numerical solution of such problems can be separated into two groups, the iterative and the noniterative methods. For linear boundary value problems, solutions can always be obtained noniteratively. For nonlinear problems, iteration is usually needed. It should be emphasized however that there are many methods by which iteration of the solution can be eliminated, thus resulting in considerable savings in computation time. Three chapters in this book are devoted to iterative methods, including the shooting method, the finite-difference method, and the integral equation method. A total of six noniterative methods will be given. Following the order of presentation, these are the methods of superposition, chasing, adjoint operators, transformation, parameter differentiation, and invariant imbedding.