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