The barycentric rational collocation method for solving semi-infinite domain problems is presented. Following the barycentric interpolation method of rational polynomial and Chebyshev polynomial. Truncation method and transformation method are presented to solve linear and nonlinear differential equation defined on the semi-infinite domain problems At last, three numerical examples are presented to test the theoretical analysis.

In this paper, the barycentric Lagrange interpolation iteration method is proposed to solve the extended FisherKolmogorov equation. Direct linearized iterative method, partial linearized iterative method and Newton linearized iterative method are introduced to deal with the nonlinear term of the equation. Then the nonlinear equation is transformed into a linear equation to solve the extended Fisher-Kolmogorov equation. The unknown function is approximated by barycentric Lagrange interpolation basis function, and the differential matrix form is obtained from iterative scheme. By combining the equation with the initial and boundary conditions, the numerical solution of the equation can be solved iteratively. Finally, the convergence analysis of the barycentric Lagrange interpolation iteration method is given, and numerical examples show that the proposed method is convergent and has higher numerical accuracy.

The hypersingular integral equation has been studied widely in boundary element methods, especially in natural boundary element methods. The asymptotic expansion of error function of composite rectangle rule for the computation of Hadamard finite-part integrals with the hypersingular kernel $ 1/\sin^{2}(x-s)$ is obtained. Extrapolation algorithm is constructed. In order to solve the hypersingular integral equation, the superconvergence point is taken as the collocation point, then the extrapolation algorithm is presented and the convergence rate of extrapolation algorithm for hypersingular integral equation is presented. At last, some numerical results are also illustrated to confirm the theoretical results and show the efficiency of the algorithms.