Stability and Approximation of Solutions in New Reproducing Kernel Hilbert Spaces on a Semi-Infinite Domain
We introduce new reproducing kernel Hilbert spaces on a trapezoidal semi-infinite domain B∞ in the plane. We establish uniform approximation results in terms of the number of nodes on compact subsets of B∞ for solutions to nonhomogeneous hyperbolic partial differential equations in one of these spaces, (Formula presented.). Furthermore, we demonstrate the stability of such solutions with respect to the driver. Finally, we give an example to illustrate the efficiency and accuracy of our results.
J. S. Hassan and D. E. Grow, "Stability and Approximation of Solutions in New Reproducing Kernel Hilbert Spaces on a Semi-Infinite Domain," Mathematical Methods in the Applied Sciences, Wiley, Jan 2021.
The definitive version is available at https://doi.org/10.1002/mma.7552
Mathematics and Statistics
Keywords and Phrases
reproducing kernel Hilbert space; stability of solutions; telegraph equation
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2021