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Approximations of the nonlinear Volterra’s population model by an efficient numerical method. (English) Zbl 1223.92047

Summary: 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 solutions for nonlinear integro-differential equations in which the integral term represents the total metabolism accumulated from time zero. The approximate analytical procedure only depends on two components. The new homotopy perturbation method was 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.

MSC:

92D25 Population dynamics (general)
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
45D05 Volterra integral equations
45J05 Integro-ordinary differential equations
65L03 Numerical methods for functional-differential equations
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