On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y₀, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

• A. M. Sagir

• Block Method
• Hybrid
• Linear Multistep
• Self starting
• Third Order Ordinary Differential Equations.

[1] S.O. Fatunla, Block Method for Second Order Initial Value Problem. International Journal of Computer Mathematics, England. Vol. 4, 1991, pp 55 – 63.
[2] S.O. Fatunla, Higher Order parallel Methods for Second Order ODEs. Proceedings of the fifth international conference on scientific computing, 1994, pp 61 –67.
[3] J. D. Lambert, Computational Methods in Ordinary Differential Equations (John Willey and Sons, New York, USA, 1973).
[4] P. Onumanyi, D.O. Awoyemi, S.N. Jator and U.W. Sirisena, New linear Multistep with Continuous Coefficient for first order initial value problems. Journal of Mathematical Society, 13, 1994, pp 37 – 51.
[5] R.L. Brown, Some Characteristics Multistep Multi-derivative Integration Formulas. SIAM Journal of Numerical Analysis. 1974, 14:992 – 993.
[6] D.O. Awoyemi, A class of Continuous Stormer – Cowell Type Methods for Special Second Order Ordinary Differential Equations, Journal of Nigerian Mathematical Society. 1998, Vol. 5, Nos. 1 & 2, pp100 – 108
[7] P. Henrici, Discrete Variable Methods for ODEs. (John Willey New York U.S.A, 1962).