Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model

TL;DR

This paper introduces a collocation method using compactly supported radial basis functions to efficiently solve Volterra's population model, a nonlinear integro-differential equation, demonstrating good accuracy and convergence.

Contribution

It presents a novel application of CSRBF-based collocation to solve Volterra's population model, reducing it to algebraic equations with proven accuracy.

Findings

Achieved high accuracy in numerical solutions

Demonstrated good convergence rates

Validated method with residual norm 2

Abstract

In this paper, indirect collocation approach based on compactly supported radial basis function is applied for solving Volterras population model. The method reduces the solution of this problem to the solution of a system of algebraic equations. Volterras model is a non-linear integro-differential equation where the integral term represents the effect of toxin. To solve the problem, we use the well-known CSRBF: Wendland3,5. Numerical results and residual norm 2 show good accuracy and rate of convergence.