Open Access

ABSTRACT

New Basis Functions and Their Applications to PDEs

Haiyan Tian¹, Sergiy Reustkiy², C.S. Chen¹

1 Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406
2 Magnetism Division, Institute of Electrodynamics, National Academy of Science of Ukraine, Industrialnaya St., 19, 61106 Kharkov, Ukraine

The International Conference on Computational & Experimental Engineering and Sciences 2007, 3(4), 169-176. https://doi.org/10.3970/icces.2007.003.169

Abstract

We introduce a new type of basis functions in this paper to approximate a scattered data set. We test our basis functions on recovering the well-known Franke's function given by scattered data. We then use these basis functions in Kansa's method for solving Helmholtz equations. To demonstrate our proposed approach, we compare the numerical solutions with analytic solutions. The numerical results show that our approach is accurate and efficient.

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