Solution of a model describing biological species living together using the variational iteration method

In this work, a system of two nonlinear integro-differential equations which arises in biology is considered and the well-known variational iteration method is implemented for finding the solution of this system. This method is based on the incorporation of a general Lagrange multiplier in the const...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 48; no. 5; pp. 685 - 699
Main Authors: Shakeri, Fatemeh, Dehghan, Mehdi
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.09.2008
Elsevier Science
Subjects:
Adomian decomposition method
Calculus of variations and optimal control
Difference and functional equations, recurrence relations
Exact sciences and technology
Integro-differential equation
Mathematical analysis
Mathematical biology
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Pseudospectral Legendre method
Sciences and techniques of general use
The equilibrium state of two species living together
Variational iteration method
Variational iteration method
Mathematical biology
Integro-differential equation
The equilibrium state of two species living together
Pseudospectral Legendre method
Adomian decomposition method
Differential equation
Decomposition method
Optimization method
Iteration
Difference equation
Implementation
Non linear equation
Lagrange multiplier
Mathematical model
Integrodifferential equation
Computer aided analysis
Linearization
Mathematical programming
Transcendental equation
Recurrence relation
Functional equation
Non linear system
Discretization method
Exact solution
Numerical analysis
Scientific computation
Pseudospectral method
Applied mathematics
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:In this work, a system of two nonlinear integro-differential equations which arises in biology is considered and the well-known variational iteration method is implemented for finding the solution of this system. This method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This technique reduces the volume of calculations by not requiring discretization of the variables, linearization or small perturbations and constructs a sequence which converges to the exact solution rapidly. Also a numerical technique based on the pseudospectral Legendre method is developed to solve the model. Several test problems are given and the results are compared with Adomian decomposition method and the variational iteration technique.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2007.11.012