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Zbl 1222.65150
Parand, K.; Abbasbandy, S.; Kazem, S.; Rad, J.A.
A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 11, 4250-4258 (2011). ISSN 1007-5704

Summary: Two common collocation approaches based on radial basis functions (RBFs) are considered; one is computed through the differentiation process (DRBF) and the other one is computed through the integration process (IRBF). We investigate these two approaches to the Volterra's population model which is an integro-differential equation without converting it to an ordinary differential equation. To solve the problem, we use four well-known radial basis functions: Multiquadrics, inverse multiquadrics, Gaussian and hyperbolic secant which is a newborn RBF. Numerical results and residual norm $(\parallel R(t) \parallel ^2)$ show good accuracy and rate of convergence of two common approaches.

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
92D25 Population dynamics

Keywords: integro-ordinary differential equation; Volterra's population model; collocation method; radial basis functions; multiquadrics; inverse multiquadrics; Gaussian; hyperbolic secant; numerical results

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Zentralblatt MATH Berlin [Germany]