A Class of Boundary Value Problems Arising in Mathematical Physics: A Green's Function Fixed-point Iteration Method

This paper presents a method based on embedding Green's function into a well-known fixed-point iteration scheme for the numerical solution of a class of boundary value problems arising in mathematical physics and geometry, in particular the Yamabe equation on a sphere. Convergence of the numerical method is exhibited and is proved via application of the contraction principle. A selected number of cases for the parameters that appear in the equation are discussed to demonstrate and confirm the applicability, efficiency, and high accuracy of the proposed strategy. The numerical outcomes show the superiority of our scheme when compared with existing numerical solutions.