A collocation method for solving some integral equations in distributions
This work provides a numerical method for a specific class of integral equations, but it is incremental as it extends existing collocation techniques to a particular kernel type.
The authors develop a collocation method for solving integral equations with kernels that are positive rational functions of selfadjoint elliptic operators, demonstrating efficiency and stability through numerical examples.
A collocation method is presented for numerical solution of a typical integral equation Rh :=\int_D R(x, y)h(y)dy = f(x), x ε D of the class R, whose kernels are of positive rational functions of arbitrary selfadjoint elliptic operators defined in the whole space R^r, and D \subset R^r is a bounded domain. Several numerical examples are given to demonstrate the efficiency and stability of the proposed method.