Numerical solution of a certain type of integral equations on the real half-line
For researchers working on numerical solutions of integral equations with mixed finite and infinite intervals, this provides a theoretically grounded method, but it is an incremental contribution to a specialized domain.
The paper develops a numerical method for solving a system of nonlinear integral equations on the real half-line, proving convergence and rate of convergence. The method discretizes the problem into an infinite-dimensional nonlinear system and shows that finite truncations approximate the solution.
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the convergence and the rate of convergence of our method. The discretization results in an infinite-dimensional nonlinear system, and we also prove results on the approximation of the solution of the infinite-dimensional system by solution of finite truncations.