A discrete collocation technique using the thin plate splines for solving a certain class of integro-differential equations arising in biology models

Abstract The primary motivation of the current article is to study an approximate algorithm to solve a type of Volterra integro-differential equations involving nonlinear terms. These integro-differential equations have been utilized to simulate several realistic modelling emanated in biological sciences, for example, the growth model of the toxins' cumulative effects on a population residing in a closed system. Thin plate splines (TPSs), known as a subclass of radial basis functions (RBFs) independent of the shape parameter, create an efficient scheme to interpolate a function. Due to this desirable property, we use the discrete collocation approach with the TPS basis for estimating the solution of mentioned integro-differential equations. Furthermore, the Gauss-Legendre integration formula is utilized to calculate the integrals emerging in the scheme. Remarkably, the algorithm of the offered approach can be comfortably performed on a PC with typical specifications derived from the simplicity of using TPSs. The researchers also investigate the convergence of the presented scheme. Some test examples including Volterra integro-differential equations are considered to make sure the veracity of the proposed scheme and the validity of the theoretical error analysis. MSC (2020): 45D05; 45J05; 92-08;92D25;