Improved Numerical Methods And The Numerical Solution Of The Beam Equation

In recent years, numerical methods for differential boundary value problems have been attracted many authors, and as two basic methods, the difference methods and shooting method are well known for their simple applications. For linear boundary value problems, special boundary conditions may provide some helpful conditions to find the numerical solution for the problem discussed. This thesis were concerned with improving the above two methods according to the speciality of the problems. On the one hand, we obtained the method so called mixed-shooting method, on the other hand, we generalized the classical difference method to obtain the new method so called quasi-difference method, these two methods improved the order of the calculation error. Some applications shown the advantages of the methods.