Solving The Parallel Block Method Of Second Order Ordinary Differential Equations

Second-order ordinary differential equations arise in a wide variety of scientific and engi-neering applications, including celestial mechanics, theoretical physics and chemistry, electronicsand semi-discretisation of partial differential equation. Because of the complexity of the second-order ordinary differential equations, it is quite difficult to obtain their analytic solution and hencenecessary to study their numerical methods.This thesis concerns with numerical methods of the second-order ordinary differential equa-tions y (x) = f(x,y) and their numerical stability property. In the first part, a class of parallelblock methods which are suitable for integrating these equations on parallel computers are pro-posed. The convergence of such methods is studied and their lowest attainable convergence ordershave been obtained. In the second part, we introduce a definition of P-stability of parallel blockmethods based on the test equation y (x) = ?λ2y. Then sufficient conditions for the 2?, 3?and 4-dimensional block methods to be P-stable are established. Numerical experiments are con-ducted to verify our theoretic results.