Exponential Fitting Parallel Multivalue Hybrid Methods For The Stiff Oscillatory Problems

Stiff oscillatory problems are involved in various fields of modern science and technology. The research on its numerical methods has wide spread and promising prospect. Due to its two-sided characteristics, namely, stiffness and oscillation, it is rather difficult and challenging to obtain highly efficient numerical solving, which has been attracting many scholars' attention for a long time. In 2002, Li Shoufu proposed parallel multi-value hybrid methods(PMHMs) to solve the stiff problems, which are proved to be very effective and superior. To better solve stiff oscillatory problems, we explore the exponential fitting algorithms of parallel multi-value hybrid methods.This thesis, constructs steps 2-4 exponential fitting algorithms of parallel multi-value hybrid methods. By analyzing their O-stability, it is shown that a kind of exponential fitting methods of parallel multi-value hybrid methods namely EF-I-1 and EF-I-2 is unstable in left half complex plane while the new kind such as EF-II-2 and EF-II-3 shows good O-stability and absolute stability. Then these algorithms are extended to vector space to promote the application of these algorithms. Meanwhile, this thesis discusses the coefficient computation of the new methods. Numerical examples show the high efficiency of the proposed methods and show the new algorithms are more effective than the corresponding PMHM methods for stiff oscillatory problems.