Abstract
In this study, a new solution scheme for the partial differential equations with variable coefficients defined on a large domain, especially including infinities, has been investigated. For this purpose, a spectral basis, called exponential Chebyshev (EC) polynomials, has been extended to a new kind of double Chebyshev polynomials. Many outstanding properties of those polynomials have been shown. The applicability and efficiency have been verified on an illustrative example.MSC:35A25.
Highlights
The importance of special functions and orthogonal polynomials occupies a central position in the numerical analysis
We have shown the extension of the exponential Chebyshev (EC) polynomial method to multivariable case, especially, to two-variable problems
5 Conclusion In this article, a new solution scheme for the partial differential equation with variable coefficients defined on unbounded domains has been investigated and EC polynomials have been extended to double EC polynomials to solve multi-variable problems
Summary
The importance of special functions and orthogonal polynomials occupies a central position in the numerical analysis. All of the above studies are considered on the interval [– , ] in which Chebyshev polynomials are defined This limitation causes a failure of the Chebyshev approach in the problems that are naturally defined on larger domains, especially including infinity. Parand et al and Sezer et al successfully applied spectral methods to solve problems on semi-infinite intervals [ , ]. These approaches can be identified as the methods of rational Chebyshev Tau and rational Chebyshev collocation, respectively. This kind of extension fails to solve all of the problems over the whole real domain. We have shown the extension of the EC polynomial method to multivariable case, especially, to two-variable problems
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