Abstract
In this work, an orthogonal polynomial with weight function w(x) =x2 + x + 1 in the interval [-1, 1] was constructed and used as the basis function to develop block methods, using collocation and interpolation approach. An efficient class of continuous and discrete numerical integration schemes of implicit hybrid form for third-order problems were developed and successfully implemented. Three different problems were solved with these schemes and they performed favourably. The investigation, using the appropriate existing theorems, shows that the methods are consistent, zero-stable and hence, convergent.
Publisher
Nigerian Society of Physical Sciences
Subject
General Physics and Astronomy,General Mathematics,General Chemistry
Reference24 articles.
1. R. A. Bun & Y. D. Vasil’yev, “A numerical method for solving diferential equations of any orders”, Journal of Computer Mathematical Physics 32 (1992) 3.
2. F. L. Joseph, R. B. Adeniyi & E. O. Adeyefa, “A Collocation Technique for Hybrid Block Methods with a Constructed Orthogonal basis for Second Order Ordinary Differential Equations”, Global Journal of Pure and Applied Mathematics 14 (2018) 4.
3. E. O. Adeyefa, “A Model for Solving First, Second and Third Order IVPs Directly”, Int. J. Appl. Comput. Math. 7 (2021) 131. https://doi.org/10.1007/s40819-021-01075-6
4. O. E. Abolarin, J. O. Kuboye, E. O. Adeyefa & B. O. Ogunware “New efficient numerical model for solving second , third and fourth order ordinary differential equations directly”, Gazi University Journal of Science 33 (2020) 4.
5. J. Sunday, G. M. Kumleng, N. M. Kamoh, J. A. Kwanamu, Y. Skwame & O. Sarjiyus, “Implicit Four-Point Hybrid Block Integrator for the Simulations of Stiff Models”, J. Nig. Soc. Phys. Sci. 4 (2022) 287. https://doi.org/10.46481/jnsps.2022.777