Interpolation for nonlinear BVP in circular membrane with known upper and lower solutions

A successive nonextrapolatory linear interpolation is described to solve a singular two-point boundary value problem arising in circular membrane theory. The problem is associated with a second-order nonlinear ordinary differential equation for which the upper and lower bounds of the solution is analytically established/known. The importance and the scope of these bounds in solving the problem is stressed. Also depicted graphically are the lower and upper solutions as well as the true and iterated solutions. In addition, discussed are the reasons why linear interpolation, and not nonlinear interpolation or bisection which are possible procedures, has been employed.