Welcome to American Journal of Numerical Analysis

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.

ISSN (Print): 2372-2118

ISSN (Online): 2372-2126

Editor-in-Chief: Emanuele Galligani

Website: http://www.sciepub.com/journal/AJNA

   

Article

Quartic B – Spline Method for Solving a Singular Singularly Perturbed Third-Order Boundary Value Problems

1Department of Mathematics Jaypee University of Engineering & Technology Guna-473226(M.P) India


American Journal of Numerical Analysis. 2015, 3(1), 18-24
doi: 10.12691/ajna-3-1-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Hradyesh Kumar Mishra, Sonali saini. Quartic B – Spline Method for Solving a Singular Singularly Perturbed Third-Order Boundary Value Problems. American Journal of Numerical Analysis. 2015; 3(1):18-24. doi: 10.12691/ajna-3-1-3.

Correspondence to: Hradyesh  Kumar Mishra, Department of Mathematics Jaypee University of Engineering & Technology Guna-473226(M.P) India. Email: hk.mishra@juet.ac.in

Abstract

In this paper, we study the numerical solution of singular singularly perturbed third-order boundary value problems (BVPs) by using Quartic B-spline method. An efficient algorithm is presented here to solve the approximate solution of the given problem. To understand our method, we introduce the Quartic B-spline basis function in the form of at the different knots. After that we derive our method by using numerical difference formulas to construct the approximate values. Then we use the linear sequence of Quartic B-spline to get the numerical solution of the system of equations. These systems of equations are solved by using MATLAB. Three examples are illustrated to understand the present method.

Keywords

References

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Article

Initial Value Method Extended for General Singular Perturbation Problems

1Department of Mathematics, Osmania University College For Women, Hyderabad, Telangana, India

2Department of Mathematics, National Institute of Technology, Warangal, Telangana, India


American Journal of Numerical Analysis. 2015, 3(1), 25-29
doi: 10.12691/ajna-3-1-4
Copyright © 2015 Science and Education Publishing

Cite this paper:
Loka Pavani, Y. N. Reddy. Initial Value Method Extended for General Singular Perturbation Problems. American Journal of Numerical Analysis. 2015; 3(1):25-29. doi: 10.12691/ajna-3-1-4.

Correspondence to: Y.  N. Reddy, Department of Mathematics, National Institute of Technology, Warangal, Telangana, India. Email: ynreddy_nitw@yahoo.com

Abstract

In this paper the initial value method is extended for solving singularly perturbed two point boundary value problems with internal and terminal layers. It is distinguished by the following fact: The given singularly perturbed boundary value problem is replaced by two first order initial value problems. These first order problems are solved using Runge Kutta method. Model example for each is solved to demonstrate the applicability of the method.

Keywords

References

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Article

Analysis of Fractional Splines Interpolation and Optimal Error Bounds

1Faculty of Science and Science Education, School of Science Education, Sulaimani Univ., Sulaimani, Iraq


American Journal of Numerical Analysis. 2015, 3(1), 30-35
doi: 10.12691/ajna-3-1-5
Copyright © 2015 Science and Education Publishing

Cite this paper:
Faraidun K. Hamasalh, Pshtiwan O. Muhammad. Analysis of Fractional Splines Interpolation and Optimal Error Bounds. American Journal of Numerical Analysis. 2015; 3(1):30-35. doi: 10.12691/ajna-3-1-5.

Correspondence to: Faraidun  K. Hamasalh, Faculty of Science and Science Education, School of Science Education, Sulaimani Univ., Sulaimani, Iraq. Email: faraidunsalh@gmail.com

Abstract

This paper presents a formulation and a study of three interpolatory fractional splines these are in the class of mα, m = 2, 4, 6, α = 0:5. We extend fractional splines function with uniform knots to approximate the solution of fractional equations. The developed of spline method is to analysis convergence fractional order derivatives and estimating error bounds. We propose spline fractional method to solve fractional differentiation equations. Numerical example is given to illustrate the applicability and accuracy of the methods.

Keywords

References

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[12]  A. K. Varma and G. Howell, Cantor-type cylindrical coordinate method for differential equations with local fractional derivatives, Physics Letters A, 377 (28) (2013) 1696-1700.
 
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