A Green element method for fourth order ordinary differential equations
Transformed two-point boundary value problems (BVPs) for the fourth order ordinary differential equations with a positive coefficient multiplying at least one of derivative terms are solved with the Green element method. The given problem is transformed into two-coupled second order BVPs amenable to suitable boundary conditions. The integral equations that arise by applying the singular integral theory are solved in the discretized problem domain with linear interpolation in space. The solutions for the two component equations are then combined to obtain a complete solution for the whole fourth order BVP. The effects of different types of loadings, excitations and boundary conditions are considered, and in each case, the results are found to illustrate the Green element method and demonstrate its advantages.
fourth order ordinary differential equation integral equations green element method (gem)