Numerical Approximation of the SEIR Epidemic Model Using the Variational Iteration Orthogonal Collocation Method and Mamadu-Njoseh Polynomials

Abstract

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

An Error Analysis of Implicit Finite Difference Method with Mamadu-Njoseh Basis Functions for Time Fractional Telegraph Equation

“…Mamadu-Njoseh polynomials (MNP) are orthogonal polynomials developed by Njoseh and Mamadu [12] for seeking the approximate solution of many linear and nonlinear problems in the field of applied mathematics. The polynomials were constructed in the interval [-1,1] with respect to the weight function These polynomials so far has contributed so much in seeking the approximate solutions of integral equations, boundary value problems, singular initial value problems in ordinary differential equation, integro-differential equation, delay differential equations.…”