Efficient Iterative Methods for Solving the SIR Epidemic Model

Abstract

In this article, the numerical and approximate solutions for the nonlinear differential equation systems, represented by the epidemic SIR model, are determined. The effective iterative methods, namely the Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM), and the Banach contraction method (BCM), are used to obtain the approximate solutions. The results showed many advantages over other iterative methods, such as Adomian decomposition method (ADM) and the variation iteration method (VIM) which were applied to the non-linear terms of the Adomian polynomial and the Lagrange multiplier, respectively. Furthermore, numerical solutions were obtained by using the fourth-orde Runge-Kutta (RK4), where the maximum remaining errors showed that the methods are reliable. In addition, the fixed point theorem was used to show the convergence of the proposed methods. Our calculation was carried out with MATHEMATICA®10 to evaluate the terms of the approximate solutions.

Stability Analysis and Assortment of Exact Traveling Wave Solutions for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

“…In this section, the results from equations ( 5) and ( 8) are compared with the standard hyperbolic tanh function method from equation ( 14) in Wazwaz et al [11] and presented in Table 1. Furthermore, the solutions of modern extension of the hyperbolic tanh function method with respect to equation ( 5) are more diverse and extensive, compared to the one in equation (8). Based to the conditions of stability, Equations ( 43) and ( 24) are stable in the interval [0, 2], while Equation ( 26) is unstable in the interval [-5, 5].…”

Solving Nonlinear Boundary Value Problem Arising of Natural Convection Porous Fin By Using the Haar Wavelet Collocation Method and Temimi and Ansari Method

“…( ) ∫ ( ) (13) We now calculate the integral of the Haar wavelet equation (10) and they are given by:…”

“…Each coefficient is associated with an accuracy level and a point in the time field. The Haar wavelet coefficients are got by converting the differential equation and its boundary conditions into a system of algebraic equations, which eventually solve the proposed problem in this paper with semi-analytically method namely the Temimi and Ansari method (TAM), which is used to solve linear and non-linear equations [9] and [10]. The wavelet coefficients were calculated by the numerical method was calculated using MATHEMATICA 11 SOFTWARE.…”

The Operational Matrices Methods for Solving Falkner-Skan Equations

“…After writing 𝑦(𝑥) and its derivatives in Eqs. ( 16) and (17) in terms of operational matrices, the collocation nodes Eq. ( 8) are substituted instead of each x to obtain the system of nonlinear algebraic equations: 0.005000000000000001 − 2. 𝑐 1 2 + 12𝑐 0 𝑐 2 − 6. 𝑐 2 2 + 120𝑐 3 + 30. 𝑐 0 𝑐 3 + 13.5𝑐 1 𝑐 3 − 11.25𝑐 2 𝑐 3 − 13.40625𝑐 3 2 = 0, 𝑐 0 − 𝑐 1 + 𝑐 2 − 𝑐 3 = 0, 2𝑐 1 − 6𝑐 2 + 12𝑐 3 = 0.9, 12𝑐 2 − 60𝑐 3 = −0.832666.…”

“…The nonlinear system of the smoking habit model was studied by analytical methods such as ADM and VIM, and numerically by the finite difference method, and the Runge-Kutta method [16]. Also, the epidemic model SJR was solved using DJM, TAM and BCM [17].…”