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- Title
Spectral Methods for Solution of Differential and Functional Equations.
- Authors
Varin, V. P.
- Abstract
An operational approach developed earlier for the spectral method that uses Legendre polynomials is generalized here for arbitrary systems of basis functions (not necessarily orthogonal) that satisfy only two conditions: the result of multiplication by or of differentiation with respect to is expressed in the same functions. All systems of classical orthogonal polynomials satisfy these conditions. In particular, we construct a spectral method that uses Chebyshev polynomials, which is most effective for numerical computations. This method is applied for numerical solution of the linear functional equations that appear in problems of generalized summation of series as well as in the problems of analytical continuation of discrete maps. We also demonstrate how these methods are used for solution of nonstandard and nonlinear boundary value problems for which ordinary algorithms are not applicable.
- Subjects
FUNCTIONAL differential equations; NUMERICAL solutions to functional equations; NONLINEAR boundary value problems; CHEBYSHEV polynomials; ORTHOGONAL polynomials; QUADRATIC equations
- Publication
Computational Mathematics & Mathematical Physics, 2024, Vol 64, Issue 5, p888
- ISSN
0965-5425
- Publication type
Article
- DOI
10.1134/S0965542524700222