Article http://dx.doi.org/10.26855/jamc.2021.06.001

Reproducing Kernel Function for Sturm-Liouville Problem with Variable Coefficients


Hossam A. Ghany1,*, Ashraf Fathallah2

1Department of Mathematics, Faculty of Technology, Helwan University, Cairo, Egypt.

2Department of Mathematics, Misr International University, Cairo, Egypt.

*Corresponding author: Hossam A. Ghany

Published: April 12,2021


This work is committed to find the analytical solution of the versatile Sturm-Liouville equation with variable coefficients by kernelization approach. The introduced generated reproducing kernel Hilbert space (RKHS) structure is subjugated to represent the solution of such problems over the suggested kernel Hilbert space. The advancement of the suggested kernel is built on the matrix structure of the Strum-Liouville operator and the Gram-Schmidt orthogonalization to construct an orthonormal sequences in an inner product Hilbert space. We exhibit the legitimacy of the formalized reproducing kernel Hilbert space to the reckoned Sturm-Liouville differential equation with variable coefficients. Uniform convergence of the approximated solution retaining the recommended scheme is surveyed. The envisaged RHKS, the deployed Sturm-Liouville operator and the analytical solution of the aimed problem are instituted to show the recital of the recommended scheme.


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How to cite this paper

Reproducing Kernel Function for Sturm-Liouville Problem with Variable Coefficients

How to cite this paper: Hossam A. Ghany, Ashraf Fathallah. (2021) Reproducing Kernel Function for Sturm-Liouville Problem with Variable Coefficients. Journal of Applied Mathematics and Computation5(2), 68-72.

DOI: http://dx.doi.org/10.26855/jamc.2021.06.001