Prelude to hopf bifurcation in an epidemic model: Analysis of a characteristic equation associated with a nonlinear Volterra integral equation

1982 ◽  
Vol 14 (1) ◽  
pp. 117-127 ◽  
Author(s):  
O. Diekmann ◽  
R. Montijn
Keyword(s):  
Integral Equation ◽  
Hopf Bifurcation ◽  
Characteristic Equation ◽  
Volterra Integral Equation ◽  
Epidemic Model ◽  
Model Analysis ◽  
Nonlinear Volterra Integral Equation

scholarly journals AN APPROXIMATE SOLUTION OF TWO DIMENSIONAL NONLINEAR VOLTERRA INTEGRAL EQUATION USING NEWTON-KANTOROVICH METHOD

2014 ◽  
Vol 35 (1) ◽  
pp. 37-42 ◽  
Author(s):  
Hameed Husam Hameed ◽  
Z. K. Eshkuvatov ◽  
N.M.A. Nik Long
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Volterra Integral Equation ◽  
Two Dimensional ◽  
Kantorovich Method ◽  
Nonlinear Volterra Integral Equation

scholarly journals Solving volterra integral equation via nonlinear programming

2016 ◽  
Vol 5 (4) ◽  
pp. 192
Author(s):  
Jamal Othman
Keyword(s):  
Integral Equation ◽  
Nonlinear Programming ◽  
Volterra Integral Equation ◽  
Least Square ◽  
Nonlinear Programming Problem ◽  
Programming Technique ◽  
New Approach ◽  
Nonlinear Volterra Integral Equation ◽  
Limited Memory ◽  
Quasi Newton

In this paper we propose an approach to find approximate solution to the nonlinear Volterra integral equation of the second type through a nonlinear programming technique by firstly converting the integral equation into a least square cost function as an objective function for an unconstrained nonlinear programming problem which solved by a nonlinear programming technique (The preconditioned limited- memory quasi-Newton conjugates, gradient method) and as far as we read this is a new approach in the ways of solving the nonlinear Volterra integral equation. We use Maple 11 software as a tool for performing the suggested steps in solving the examples.

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

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