  In this work, we consider a boundary value problem for nonlinear triharmonic
equation. Due to the reduction of nonlinear boundary value problems to operator
equation for nonlinear terms we establish the existence, uniqueness and
positivity of solution. More importantly, we design an iterative method at both
continuous and discrete level for numerical solution of the problem. An
analysis of actual total error of the obtained discrete solution is made. Some
examples demonstrate the applicability of the theoretical results on
qualitative aspects and the efficiency of the iterative method.
