scholarly journals An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm

2020 ◽  
Vol 17 (5) ◽  
pp. 5752-5801
Author(s):  
Benjamin Wacker ◽  
◽  
Jan Schlüter ◽  
Keyword(s):  
Numerical Solution ◽  
Model Theory ◽  
Sir Model ◽  
Solution Algorithm ◽  
Age And Sex

scholarly journals Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Equation System ◽  
Solution Algorithm ◽  
Basis Functions ◽  
Algebraic Equations ◽  
Parabolic Pdes ◽  
Linear Partial Differential Equations ◽  
Type Boundary

An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

Numerical Treatment of the Fractional Modeling on Susceptible-Infected-Recovered Equations with a Constant Vaccination Rate by Using GEM

2019 ◽  
Vol 20 (1) ◽  
pp. 69-75
Author(s):  
M. M. Khader ◽  
M. Adel
Keyword(s):  
Numerical Solution ◽  
Numerical Solutions ◽  
Sir Model ◽  
Vaccination Rate ◽  
Euler Method ◽  
Numerical Results ◽  
Numerical Treatment ◽  
Generalized Euler Method ◽  
Fractional Modeling

AbstractHere, we introduce a numerical solution by using the generalized Euler method for the (Caputo sense) fractional Susceptible-Infected-Recovered (SIR) model with a constant vaccination rate. We compare the obtained numerical solutions with those solutions by using the RK4. Hence, the obtained numerical results of the SIR model show the simplicity and the efficiency of the proposed method.

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