1,721,082 research outputs found
Boundary value methods for the numerical solution of boundary value problems in differential-algebraic equations
No full textSoftware for Boundary Value Problems, http://pitagora.dm.uniba.it/~mazzia/bvp/index.html
No full text
Solving ordinary differential equations by generalized Adams methods: properties and implementation techniques
No full textGeneralized Adams methods of order 3, 5, 7 and 9 are used to find numerical solutions of initial value problems. The effectiveness of these methods for the treatment of stiff problems is shown on the basis of their attractive properties and an efficient technique to deal with the algebraic nonlinear systems representing the discrete counterpart of the continuous problem. Numerical examples are also presented in which an experimental code based on these methods is compared with two well known codes for ODEs. The numerical results are quite satisfactory and suggest that these methods may have a useful role in the solution of stiff ODEs
The BS class of Hermite spline quasi-interpolants on nonuniform knot distributions
No full textThe BS Hermite spline quasi-interpolation scheme is presented. It is related to the continuous extension of the BS linear multistep methods, a class of Boundary Value Methods for the solution of Ordinary Differential Equations. In the ODE context, using the numerical solution and the associated numerical derivative produced by the BS methods, it is possible to compute, with a local approach, a suitable spline with knots at the mesh points collocating the differential equation at the knots and having the same convergence order as the numerical solution. Starting from this spline, here we derive a new quasi-interpolation scheme having the function and the derivative values at the knots as input data. When the knot distribution is uniform or the degree is low, explicit formulas can be given for the coefficients of the new quasi-interpolant in the B-spline basis. In the general case these coefficients are obtained as solution of suitable local linear systems of size 2d×2d, where d is the degree of the spline. The approximation order of the presented scheme is optimal and the numerical results prove that its performances can be very good, in particular when suitable knot distributions are used
Convergence and stability of multistep methods solving nonlinear Initial Value Problems
No full textConvergence and stability of initial and boundary value multistep methods are analyzed for a class of nonlinear problems, satisfying a one-sided Lipschitz condition. The linear multistep methods are recast to handle the numerical solution globally on the time interval. This allows us to use the theory of Toeplitz matrices to show that, under suitable assumptions, global properties of the exact solution are preserved by its numerical approximation. In particular, a new concept of stability, which avoids the unpleasant passage to one-leg methods, is introduced
A parallel Gauss-Seidel method for block tridiagonal linear systems
No full textA parallel variant of the block Gauss-Seidel iteration is presented for the solution of Mock 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 initial value problems when solved by means of boundary value methods and from elliptic partial differential equations
Quadrature formulas descending from BS Hermite spline quasi-interpolation
No full textTwo new classes of quadrature formulas associated to the BS Boundary Value Methods are discussed. The first is of Lagrange type and is obtained by directly applying the BS methods to the integration problem formulated as a (special) Cauchy problem. The second descends from the related BS Hermite quasi-interpolation approach which produces a spline approximant from Hermite data assigned on meshes with general distributions. The second class formulas is also combined with suitable finite difference approximations of the necessary derivative values in order to define corresponding Lagrange type formulas with the same accuracy. (C) 2012 Elsevier B.V. All rights reserved
- …
