Analysis of radial basis collocation method and quasi-Newton iteration for nonlinear elliptic problems
نویسندگان
چکیده
This work presents a global radial basis collocation combining with the quasiNewton iteration method for solving semilinear elliptic partial differential equations. A convergence analysis for such a meshfree discretization has been established. The main result is that there exists an exponential convergence rate with respect to the number and the shape of the radial basis functions. In addition, a superlinear convergence rate with respect to quasi-Newton iteration is obtained. Some results are given to illustrate the efficiency and accuracy of the proposed method.
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