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A Numerical Algorithm for the Resolution of Scalar and Matrix Algebraic Equations Using Runge-Kutta Method
Applied and Computational Mathematics
Volume 3, Issue 3, June 2014, Pages: 68-74
Received: May 3, 2014; Accepted: May 17, 2014; Published: May 30, 2014
Author
Tahar Latreche, Doctorate student in Civil Engineering, B.P. 129 Salem Lalmi, 40003 Khenchela, Algeria
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Abstract
The Runge-Kutta method is an interesting and precise method for the resolution of ordinary differential equations. Fortunately, when supposing the differentiation by any variable that the equation to solve is not variable of, and after iterations, the solution of this equation stretches to the algebraic roots of this equation. This feature of this algorithm, indeed, allows to solve precisely any scalar or matrix equation. The numerical algorithm proposed herein is an iterative procedure of the fourth-order Runge-Kutta method with an adopted precision tolerance of convergence. Also, a method to determine all the roots of the polynomial equations is presented. Some scalar and matrix algebraic equations are resolved using this proposed algorithm, and show how this algorithm featuring with an excellent precision, a good speed and a simplicity for programming to solve equations and deduct the roots.
Keywords
Algebraic Equations, Linear and Non-Linear Algebra, Elementary Equations, Polynomial Equations, Runge-Kutta Method
Tahar Latreche, A Numerical Algorithm for the Resolution of Scalar and Matrix Algebraic Equations Using Runge-Kutta Method, Applied and Computational Mathematics. Vol. 3, No. 3, 2014, pp. 68-74. doi: 10.11648/j.acm.20140303.11
References
[1]
Bird, J., (2010). Higher Engineering Mathematics. Sixth Edition, Elsevier, Ltd.
[2]
Ciarlet, P. G., and Lions, J. L., (2000). Handbook of Numerical Analysis. Vol. 7. First Edition, Elsevier Science.
[3]
Kiusalaas, J., (2005). Numerical Methods in Engineering with Python. First Edition, Cambridge University Press.
[4]
Polyanin, A. D. and Manzhrov, A. V., (2007). Handbook of Mathematics for Engineers and Scientists. First Edition, Taylor and Francis Group, LLC.
[5]
Press, W. H. et al., (2007). Numerical Recipes. Third Edition, Cambridge University Press.
[6]
Press, W. H. et al., (1997). Numerical Recipes in Fortran 77. Second Edition, Cambridge University Press.
[7]
Press, W. H. et al., (1997). Numerical Recipes in Fortran 90. Second Edition, Cambridge University Press.
[8]
Riley, K. F. et al., (2006). Mathematical Methods for Physics and Engineering. Third Edition, Cambridge University Press.
[9]
Soyeur, A. et al., (2011). Cours de Mathématiques. http://www.les-mathematiques.net
[10]
Yang, W. Y., et al., (2005). Applied Numerical Methods using Matlab. First Edition, John-Wiley and Sons, Inc.
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