ADVANCEMENTS IN LINEAR MULTI-STEP METHOD FOR SOLVING THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Etim, Uduak James; Eno John; Dr. Tombotamunoa W. J. Lawson; Udo Ukemeobong Monday

Etim, Uduak James Akwa Ibom State University, Nigeria
Eno John Akwa Ibom State Polytechnic, Ikot Osurua, Nigeria
Dr. Tombotamunoa W. J. Lawson Ignatius Ajuru University of Education, Port Harcourt, Nigeria.
Udo Ukemeobong Monday Akwa Ibom State University, Nigeria

Keywords: Four-Step Method, Third-Order Ordinary Differential Equations, Truncation Error, Taylor's Series, Consistency, Zero Stability, Convergence, Absolute Stability, Numerical Analysis.

Abstract

This work addresses the development of four step linear multi-step methods for the solution

of third order ordinary differential equations. The approach requires the construction of a truncation error term and expanding it in Taylor’s series. The resulting FOUR step method are analysed to show that it is consistent, zero stable and hence convergent with good interval of absolute stability.Thus the new method satisfies the minimum condition for a linear multi-step method to be acceptable. The technique of derivation employed in this work is easier and more adaptable than those of collocation

Author Biographies

Etim, Uduak James, Akwa Ibom State University, Nigeria

Department of Mathematics

Eno John, Akwa Ibom State Polytechnic, Ikot Osurua, Nigeria

Department of General Studies

Dr. Tombotamunoa W. J. Lawson, Ignatius Ajuru University of Education, Port Harcourt, Nigeria.

Department of Mathematics/Statistics,

Udo Ukemeobong Monday, Akwa Ibom State University, Nigeria

Department of Mathematics

References

[1] Ismail, M. S., El-Tawil, M. A., & El-Danaf, T. S. (2014). On the Construction of Linear Multistep Methods.Abstract and Applied Analysis, 2014, 1-7.
[2] Burden, R. L., & Faires, J. D. (2016). Numerical Analysis.Cengage Learning.
[3] Butcher, J. C. (2008). Numerical Methods for Ordinary Differential Equations.John Wiley & Sons.
[4] Ascher, U. M., & Petzold, L. R. (1998). Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations.SIAM.
[5] Hairer, E., Nørsett, S. P., &Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems.Springer-Verlag.
[6] Lambert, J. D. (1973). Computational Methods in Ordinary Differential Equations.John Wiley & Sons.
[7] Shampine, L. F., & Gordon, M. K. (1975). Computer Solution of Ordinary Differential Equations: The Initial Value Problem.W. H. Freeman and Company.