In this paper, block procedure for some k-step
linear multi-step methods, using the Legendre polynomials as the basis
functions, is proposed. Discrete methods were given which were
used in block and implemented for solving the initial value problems, being
continuous interpolant derived and collocated at grid points. Some numerical
examples of ordinary differential equations were solved using the derived
methods to show their validity and the accuracy. The numerical results obtained
show that the proposed method can also be efficient in solving such problems.
Cite this paper
Okedayo, T. G. , Owolanke, A. O. , Amumeji, O. T. and Adesuyi, M. P. (2018). Modified Legendre Collocation Block Method for Solving Initial Value Problems of First Order Ordinary Differential Equations. Open Access Library Journal, 5, e4565. doi: http://dx.doi.org/10.4236/oalib.1104565.
Kayode, S.J. (2008) An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations. International Journal of Mathematics and Mathematical Sciences, 1-10.
Awoyemi, D.O. (2005) Algorithm Collocation Approach for Direct Solution of Fourth Order Initial Value Problems of ODEs. International Journal of Computational Mathematics, 82, 271-284.
Adee, S.O., Onumanyi, P., Sirisena, U.W. and Yahaya, Y.A. (2005) Note on Starting the Numerov Method More Accurately by a Hybrid Formula of Order Four for Initial Value Problems. Journal of Computational and Applied Mathematics, 175, 369-373. https://doi.org/10.1016/j.cam.2004.06.016
Yahaya, A.M. and Badmus, Y.A. (2009) An Accurate Uniform Order 6, Block Method for Direct Solution of General Second Order Ordinary Differential Equation. Pacific Journal of Science and Technology, 10, 248-254.
Chu, M.T. and Hamilton, H. (1987) Parallel Solution of ODEs by Multiblock Methods. SIAM Journal of Scientific and Statistical Computation, 8, 342-553. https://doi.org/10.1137/0908039
Omar, Z. and Suleiman, M. (2003) Parallel R-Point Implicit Block Method for Solving Higher Order Ordinary Differential Equation Directly. Journal of Information Communication Technology, 3, 53-66.
Areo, E.A. and Adeniyi, R.B. (2013) Sixth Order Hybrid Block for the Numerical Solution of First Order Initial Value Problems. Mathematical Theory and Modelling, 82, 345-364.
