A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation

In this paper two common collocation approaches based on radial basis functions (RBFs) have been 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 on 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 (MQ), Inverse multiquadrics (IMQ), Gaussian (GA) and Hyperbolic secant (sech) which is a newborn RBF. Numerical results and residual norm (‖R(t)‖2)(‖R(t)‖2) show good accuracy and rate of convergence of two common approaches.

► Two collocation approaches based on radial basis functions have been considered.
► Volterra’s Population Model is solved by using two approaches RBF.
► This model is an integro-differential equation.
► The Model solved without converting to an ordinary differential equation.