A boundary value appraoch to the numerical solution of initial value problems by means of linear multistep methods is presented. This theory is based on the study of linear difference equations when their general solution is computed by... more
A boundary value appraoch to the numerical solution of initial value problems by means of linear multistep methods is presented. This theory is based on the study of linear difference equations when their general solution is computed by imposing boundary conditions. All the main stability and convergence properties of the obtained methods are investigated abd compared to those of the classical multistep methods. Then, as an example, new itegration formulas, called extended trapezoidal rules, are derived. For any order they have the ...
Abstract The cyclic reduction algorithm is one of the fastest algorithms for the solution of tridiagonal linear systems on parallel computers. We consider an efficient version of this algorithm on distributed memory parallel computers.... more
Abstract The cyclic reduction algorithm is one of the fastest algorithms for the solution of tridiagonal linear systems on parallel computers. We consider an efficient version of this algorithm on distributed memory parallel computers. The basic idea is to divide the original system into subsystems which are solved almost independently. Communications are only needed for solving a tridiagonal system whose dimension is proportional to the number of processors. By utilizing a hypercube as topology of interconnection among the processors ...
A parallel variant of the block Gauss-Seidel iteration is presented for the solution of block tridiagonal linear systems. In this method parallel computations derive from a block reordering of the coefficient matrix similar to that of the... more
A parallel variant of the block Gauss-Seidel iteration is presented for the solution of block tridiagonal linear systems. In this method parallel computations derive from a block reordering of the coefficient matrix similar to that of the domain decomposition methods. It has been proved that the parallel Gauss-Seidel iteration has the same spectral properties of the sequential method and may be used for any sparsity pattern of the blocks of the linear system. The parallel algorithm is applied to the solution of linear systems arising from ...
Abstract High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting the problem as a first order system. Both theoretical analysis and numerical comparison with central... more
Abstract High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting the problem as a first order system. Both theoretical analysis and numerical comparison with central difference schemes of the same order show that these new methods may avoid typical oscillations and achieve high accuracy. Singular perturbation problems are taken into account to emphasize the main features of the proposed methods.
We consider the application of symmetric Boundary Value Methods to linear autonomous Hamiltonian systems. The numerical approximation of the Hamiltonian function exhibits a superconvergence property, namely its order of convergence is p+... more
We consider the application of symmetric Boundary Value Methods to linear autonomous Hamiltonian systems. The numerical approximation of the Hamiltonian function exhibits a superconvergence property, namely its order of convergence is p+ 2 for ap order symmetric method. We exploit this result to define a natural projection procedure that slightly modifies the numerical solution so that, without changing the convergence properties of the numerical method, it provides orbits lying on the same quadratic manifold as the continuous ones. A ...
