Using Maple Software To Achieve Polynomial Of Degree Five (5) From Numerov Formula

Authors

  • Williams, C. Abdul National Mathematical Center, Abuja, FCT, Nigeria
  • Madu, I. Marisa Department of Computer Science, Federal Polytechnic, Bauchi, Bauchi State, Nigeria
  • Fadele, A. Alaba Department of Computer Science, Federal Polytechnic, Bauchi, Bauchi State, Nigeria
  • Usman, Sani Department of Computer Science, Federal Polytechnic, Bauchi, Bauchi State, Nigeria

Keywords:

Degree, Software, particularly, This work was aimed at exploring the use of Maple Software

Abstract

This work was aimed at exploring the use of Maple Software, an ideal mathematical tool, particularly, in the derivation of a Numerov Method for the solution of a Second Order Ordinary Differential Equation (ODE) of the type by a polynomial of degree five on the mesh points. The result obtained agreed with the derivation of a Continuous Numerov Formula, Yahaya (2004). It was possible to use the Maple software for the symbolic computation of the matrix AX = B from the polynomial of degree five to achieve result. It also aimed at achieving a polynomial of degree five with the same initial conditions satisfied by the polynomial of degree four at . It was encouraging to compare the volume of work achieved in less time using the software than by manual computation.(paper and pen based). The result is optimal for the derivation of approximation on the three grid points . Consequently, it is justifiable to encourage the use of Maple Software in higher institutions of learning. 

References

Awoyemi, D. O. (2003). A p-stable linear multistep method for the solution of general third order ordinary differential equations. International Journal of Computer and Mathematics, 80(8), 987-993.

Awoyemi, D.O. and Kayode, S. J. (2002). An optimal order continuous multistep algorithm for initial value problems of special second order differential equations. Journal of Nigeria Association of Mathematical Physics, 6, 285-292.

Awoyemi, D. O. and Kayode, S. J. (2003). An optimal order collocation method for direct solution of initial value problems of general second order ordinary differential equations. FUTAJEET, 3, 33 - 40

Bun, R. A. and Vasil'Yev, Y. D. (1992): A numerical method for solving differential equations of any orders. Computer, Mathematics and Physics, 32(3), 317-330.

Faires, J. D. and Barden, R. L. (1993). Numerical Methods. Boston: PWS Publishing Company: 503p.

Fatokun, J. (2005). An Economized Power Series Collocation Method of order Five for Solving Initial value Problems. Journal of Natural and Applied Sciences, 1, (2), 26 - 32.

Fatokun, J. (2007). Introduction to Numerical Analysis. Lecture Notes delivered in the Department of Mathematical Sciences, Nasarawa State University, Keffi.

Fatunla, S. O. (1988). Numerical Methods for IVPs in ordinary differential equations. New York: Academic Press Inc. and Harcourt Brace Jovanovich Publishers,

Froberg, C. E. (1969). Introduction to Numerical Analysis (2nd edition). Addison - Wesley, Reading 438p.

Jacques, I. and Judd, C. J. (1987). Numerical Analysis. New York: Chapman and Hall

Kimbir, A. R. (2008). Theories of Ordinary Differential Equations. Lecture Notes delivered in the Department of Mathematical Sciences, Nasarawa State University, Keffi.

Lambert J. D. (1973). Computational Methods in Ordinary Differential Equations. New York: John Willey.

Lambert J. D. (1991). Numerical methods for ordinary differential systems of initial value problems. New York: John Wiley and Sons.

Onumanyi, P. (2008). Numerical Analysis I. Lecture Notes delivered in the Department of Mathematical Sciences, Nasarawa State University, Keffi.

Onumanyi P., Fatokun J. and Adejo B. O. (2008). Accurate Numerical Differentiation by continuous integrators for ordinary differential equations. Journal of the Nigerian Mathematical Society, 27, 69 - 90.

Quiroz Gonzalez, J. L. M. and Thompson, D. (1977). Getting started with Numerov's Method. Computer in Physics, 11 (5), 514-515.

Yahaya, Y. A. (2004), Some Theories and Application of Continuous Linear Multistep Methods for Ordinary Differential Equations. PhD Thesis, University of Jos, Jos, Nigeria.

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Published

2023-12-13

How to Cite

Abdul, W. C., Marisa, M. I., Alaba, F. A., & Sani, U. (2023). Using Maple Software To Achieve Polynomial Of Degree Five (5) From Numerov Formula . International Journal of Engineering and Mathematical Intelligence (IJEMI) , 1(1,2&3), 67–74. Retrieved from http://icidr.org.ng/index.php/Ijemi/article/view/444

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