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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| Vydáno v: | Mathematical and computer modelling Ročník 48; číslo 5; s. 685 - 699 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Elsevier Ltd
01.09.2008
Elsevier Science |
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| ISSN: | 0895-7177, 1872-9479 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Dehghan, Mehdi Shakeri, Fatemeh |
| Author_xml | – sequence: 1 givenname: Fatemeh surname: Shakeri fullname: Shakeri, Fatemeh – sequence: 2 givenname: Mehdi surname: Dehghan fullname: Dehghan, Mehdi email: mdehghan@aut.ac.ir |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Solution of a model describing biological species living together using the variational iteration method |
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