Numerical studies of algorithms for solving some differential equations

Some iterative methods are studied for solving a stiff system of two ordinary differential equations with smooth and nonsmooth initial data. Some fundamental conditions required by Sammon [5] are verified. If the high dimensional systems are considered, two-term or three-term conjugate gradient methods can be explored. According to our examples, these two methods have no significant difference in the sense of number of iterations. Finally, the Incomplete Cholesky conjugate gradient method is used to compare with the classical conjugate gradient method. In all test problems ICCG was faster than GC .