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A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation. (English) Zbl 1222.65150
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:
 65R20 Integral equations (numerical methods) 45J05 Integro-ordinary differential equations 45G10 Nonsingular nonlinear integral equations 92D25 Population dynamics (general)
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