Numerical algorithm with high accuracy for the modified Helmholtz equation with Robin boundary value problem

Abstract

In order to obtain the numerical solutions of the modified Helmholtz equation with Robin boundary conditions in two dimensions, we have developed a numerical algorithm to solve the problem, which is based on a Nyström discretization. First, the problem is transformed to a weakly-singular integral equation. Then we construct a quadrature method that achieve a convergence rate of O(h3), which has the characteristics of simple calculation and high precision. Further, the convergence of the numerical solutions is proved based on the collectively compact operators theory and the single parameter asymptotic expansion of errors with odd power O(h3) is got. From the expansion, we construct an extrapolation algorithm (EA) to further improve the accuracy of the numerical solutions. Finally, some numerical examples are presented to demonstrate the efficiency of the method.