Numerical Solution of Multiple Nonlinear Volterra Integral Equations
Provides theoretical guarantees for numerical methods in a specialized class of integral equations, but the problem is niche and the contribution is incremental.
The paper analyzes a discretization method for solving nonlinear Volterra integral equations with multiple integrals, proving existence, uniqueness, convergence, and order estimates for numerical solutions.
We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.