Approximations of the nonlinear Volterra's population model by an efficient numerical method |
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Authors: | Najeeb Alam Khan Asmat Ara Muhammad Jamil |
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Institution: | 1. Department of Mathematics, University of Karachi, , Karachi, 75270 Pakistan;2. Abdul Salam School of Mathematical Sciences, GC University, , Lahore, Pakistan;3. Department of Mathematics, NED University of Engineering & Technology, , Karachi‐, 75270 Pakistan |
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Abstract: | In this paper, we apply the new homotopy perturbation method to solve the Volterra's model for population growth of a species in a closed system. This technique is extended to give solution for nonlinear integro‐differential equation in which the integral term represents the total metabolism accumulated fromtime zero. The approximate analytical procedure only depends on two components. The newhomotopy perturbationmethodwas applied to nonlinear integro‐differential equations directly and by converting the problem into nonlinear ordinary differential equation. We also compare this method with some other numerical results and show that the present approach is less computational and is applicable for solving nonlinear integro‐differential equations and ordinary differential equations as well. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | integro‐differential equation population new homotopy perturbation method (NHPM) growth toxin |
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