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
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Tahar Latreche, Doctorate student in Civil Engineering, B.P. 129 Salem Lalmi, 40003 Khenchela, Algeria
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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.
Algebraic Equations, Linear and Non-Linear Algebra, Elementary Equations, Polynomial Equations, Runge-Kutta Method
To cite this article
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.
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