Modified Laguerre Collocation Block Method for Solving Initial Value Problems of First Order Ordinary Differential Equations
T. G. Okedayo
Department of Mathematics, Ondo State University of Science and Technology, Okitipupa, PMB 353, Ondo State, Nigeria.
O. T. Amumeji
Department of Mathematics, Ondo State University of Science and Technology, Okitipupa, PMB 353, Ondo State, Nigeria.
A. O. Owolanke *
Department of Mathematics, Ondo State University of Science and Technology, Okitipupa, PMB 353, Ondo State, Nigeria.
O. K. Ogunbamike
Department of Mathematics, Ondo State University of Science and Technology, Okitipupa, PMB 353, Ondo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, an implicit k-step linear multi-step methods using the Laguerre polynomials as the basis functions is proposed. The given discrete methods were used in block and implemented for solving the initial value problems, being continuous interpolant derived and collocated at grid points. Numerical examples of initial value problems (IVPs) of ordinary differential equations (ODEs) were solved using the derived methods, and it is observed that the results obtained converged faster and the consistency and the zero stability are validated.
Keywords: Block methods, Laguerre polynomials, collocation and convergent