ARITHMETIC AVERAGE GEOMETRIC MESH DISCRETIZATIONS FOR FOURTH AND SIXTH ORDER NONLINEAR TWO POINT BOUNDARY VALUE PROBLEMS

摘要

A third order accurate numerical method is developed for solving fourth and sixth order nonlinear ordinary differential equations with associated boundary conditions. Method is compact and uses one central and two off step geometric grids. Arithmetic average finite difference approximations have been applied for deriving new numerical scheme. The method can be easily extended to the high order (even) differential equations. The error analysis of the method has been analyzed briefly. The resulting difference equations leads to block tri-diagonal matrices and can be easily solved using block gauss-seidel algorithm. The numerical experiments with several singular and non-singular problems are conducted using proposed method. The computational results justify the reliability and efficiency of the method both in terms of order and accuracy.