A technique for the numerical solution of initial-value problems based on a class of Birkhoff-type interpolation method

Authors:
Mehdi Dehghan;S. Aryanmehr;M. R. Eslahchi
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 13
Cited 0

Two low accuracy methods for stiff systems

Applied Mathematics and Computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the convergence of He's variational iteration method

Journal of Computational and Applied Mathematics
On constructing new interpolation formulas using linear operators and an operator type of quadrature rules

Journal of Computational and Applied Mathematics
A generalization of the Lane-Emden equation

International Journal of Computer Mathematics
High-order nonlinear initial-value problems countably determined

Journal of Computational and Applied Mathematics
Parallel two-step ROW-methods for stiff delay differential equations

Applied Numerical Mathematics
On constructing new expansions of functions using linear operators

Journal of Computational and Applied Mathematics
On the numerical solution of differential equations of Lane-Emden type

Computers & Mathematics with Applications
A direct variable step block multistep method for solving general third-order ODEs

Numerical Algorithms
A class of collocation methods for numerical integration of initial value problems

Computers & Mathematics with Applications
Solution of delay differential equations via a homotopy perturbation method

Mathematical and Computer Modelling: An International Journal
Birkhoff quadrature formulae based on the zeros of Jacobi polynomials

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper a class of Birkhoff-type interpolation problems on arbitrary nodal points is studied. The explicit representation (characterization), the uniqueness and the error function are explicitly given. Furthermore, we apply the obtained Birkhoff-type interpolation method to find: (i) the numerical solution of high order initial-value problems (IVPs) and the corresponding error of this approximation, (ii) the approximation of some special functions with their explicit error functions, and (iii) new interpolatory type quadrature formulae of precision degree at least m+n-1 and m+kn-1(m,n,k@?N,n,k=2). Numerical examples are included to demonstrate the validity and applicability of the technique proposed in this paper and a comparison is made with the existing results. The results reveal that the new method is effective, simple and accurate.