Reproducing kernel methods for solving linear initial-boundary-value problems. (English) Zbl 1137.35328

Summary: In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an \(n\)-term summation. Error estimates are proved to converge to zero in the sense of the space norm, and a numerical example is given to illustrate the method.


35C10 Series solutions to PDEs
35A35 Theoretical approximation in context of PDEs
65N99 Numerical methods for partial differential equations, boundary value problems
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