A Block Integrator for the Solution of First order Ordinary Differential Equations Using Legendre Polynomial
Kaze Atsi *
Department of Mathematics, Federal University Gashua, Nigeria.
Buba Hambagda
Department of Mathematics, Federal University Gashua, Nigeria.
F. E. Ogunwuyi
Department of Mathematics, Federal University Gashua, Nigeria.
G. M. Kumleng
Department of Mathematics, University of Jos, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
A block integrator for the solution of first order ordinary differential equations using Legendre polynomial has been developed in this research. The combination of power series as the basis function and Legendre polynomial a perturbation term, has been adopted in this work, Four discrete methods for step number, k = 4, have been derived using the multi-step collocation approach at the grid points. The stability properties of the newly constructed method has been investigated and has shown to be convergence. The new method found to be suitable for computing solutions of initial value problems of first order ordinary differential. The solutions of the new block methods have been compared with the corresponding solutions of exact method and other related methods. The implementation approach adopted, contributed both in the convergence of the method.
Keywords: Aedes aegypti, Power series, scanning, egg, Legendre polynomial, chorion,, block integrator, dengue mosquito., first order ODEs, consistency