Numerical Integration of Differential Equations Occurring in Two-Point Boundary Value Problems

An accurate procedure is described for numerically solving two-point boundary value problems which contain growing solutions. The procedure involves the process of reducing the order of a differential equation when one solution is known. Two applications of the procedure are given, a fourth order differential equation with two growing solutions and a system of eighth order differential equations of motion for a hemispherical shell. In both examples before the procedure is started, the equations are rewritten as a system of first order differential equations. It was found that when solving two-point boundary value problems by the reduction of order method, first order differential equations were generally easier to work with than higher order differential equations. For both applications a computer program was developed to solve the system of differential equations.Office of Naval Research. Department of the Navy.Contract No. N00014-75-C-0164Project NR 064-18