The finite element method for nonlinear nonstandard volterra integral equations

In this work, we look at the implementation of the finite element method to a nonlinear (nonstandard) Volterra integral equation. We consider the Galerkin approach, where we choose the weight function in such a way that it takes the form of the approximate solution. We work on a uniform mesh and choose the Lagrange polynomials as basis functions. We consider the error analysis of the method. We look at a specific example to illustrate the implementation of the finite element method. Finally, we consider the estimated rate of convergence.