American Journal of Numerical Analysis
http://www.sciepub.com/journal/AJNA
American Journal of Numerical Analysis is a peer-reviewed, open access journal that publishes original research articles and review articles in all areas of numerical analysis. Numerical Analysis is called the Mathematics of Scientific Computing. More specifically, Numerical Analysis involves the study, development and analysis of methods for obtaining approximate solutions to mathematical problems. This definition does pinpoint some of the key issues in Numerical Analysis, namely, approximate solution, mathematical problems, the study, development and analysis of methods. The methods invariably are destined for use on high-speed computers and therefore three major sources of error (discretization error, approximation error, rounding error) are present in the study of numerical methods. Underlying all these sources is the general question of the stability of the solution of the problem to be solved and of the discrete ill-posedness of the problem.Science and Education Publishingen2013 Science and Education Publishing Co. Ltd All rights reserved.American Journal of Numerical Analysis
2
4
January 2014
2013 Science and Education Publishing Co. Ltd All rights reserved.
A Modification of Newton Method with Third-Order Convergence
http://pubs.sciepub.com/ajna/2/4/1
Gentian Zavalani
2014-05-09Science and Education Publishing2014-05-09429810110.12691/ajna-2-4-1
Variational Iteration Method for a Singular Perturbation Boundary Value Problems
http://pubs.sciepub.com/ajna/2/4/2
Hradyesh Kumar Mishra, Sonali saini
2014-05-19Science and Education Publishing2014-05-194210210610.12691/ajna-2-4-2
Interpolation Splines Minimizing Semi-Norm in <i>K</i><SUB><i>2</i></SUB>(<i>P</i><SUB><i>2</i></SUB>) Space
http://pubs.sciepub.com/ajna/2/4/3
K_{2}(P_{2}) space are constructed. Explicit formulas for coefficients of interpolation splines are obtained. The obtained interpolation spline is exact for the functions and . Also we give some numerical results where we showed connection between optimal quadrature formula and obtained interpolation spline in the space K_{2}(P_{2}).]]>
Kholmat M. Shadimetov, Abdullo R. Hayotov, Azamov S. Siroj
2014-05-26Science and Education Publishing2014-05-264210711410.12691/ajna-2-4-3
Optimal Quadrature Formulas with Derivative in the Space L<SUB>2</SUB><SUP>(m)</SUP>(0,1)
http://pubs.sciepub.com/ajna/2/4/4
. In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number and for any using S.L. Sobolev method which is based on discrete analogue of the differential operator. In particular, for m=2,3 optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from m=4 new optimal quadrature formulas are obtained.]]>
Abdullo R. Hayotov, Farhod A. Nuraliev, Kholmat M. Shadimetov
2014-06-09Science and Education Publishing2014-06-094211512710.12691/ajna-2-4-4