For Odes With Continuous Finite Element Methods Superconvergence And Stability Estimates

The aim of this thesis is to analyze the super-convergence and stability of continuous finite element methods which is a type of numerical me-thods solving the 1-degree lineal initial value problem of ordinary differential equation, and compare the stability of the three 4-order pre-cision numerical methods of the 1-degree initial value problem of ordinary differential equation -classical Runge-Kutta method (single step method), Adams hidden method (multiple step method), and continuous finite element method.When I analyze the superconvergence of m degree continuous finite element method, from1 add some lower terms in the reminder (R) of or-thogonal expansion in an element so that the re-mainder satisfies more orthogonality conditions in the element, and let the constructed more close to the finite element solution so I obtain the following superconvergence result: there are 0(h^2m) precision at the nodal of the element , and 0(h^m+2) precision at the m+1-degree Lobatto nodal in the element.When comparing the absolute stable distance of the above methods, I model ize the 1-degree initial value problem of ordinary differential equation to this form: u' = λu (λ is real ordinary number). We obtain the result: the absolute stable distance of the classical Runge-Kuttamethod is ,the absolute stable distanceof the Adams hidden method is , and theabsolute stable distance of the continuous finite element method is .The continuous finite element method has more broad absolute stable distance and better precision of practical computing than the others.