The Separation of Variables Method

Aleksandr A. Samarskii and Evgenii S. Nikolaev
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Aleksandr A. Samarskii: Moscow University, Department of Computational Mathematics and Cybernetics
Evgenii S. Nikolaev: Moscow University, Department of Computational Mathematics and Cybernetics

Chapter Chapter 4 in Numerical Methods for Grid Equations, 1989, pp 171-238 from Springer

Abstract: Abstract In this chapter we study variants of the method of separation of variables, which we use to solve the simplest elliptic grid equations in a rectangle. In Section 4.1 we present an algorithm for the fast Fourier transform of real and complex functions. In Section 4.2 we consider a classical variant of the method of separation of variables, using the Fourier transform algorithm. In Section 4.3 we construct a combined method, including incomplete reduction and separation of variables. We consider an application of this method to the solution of second and fourth order boundary value difference problems for Poisson’s equation. In Section 4.4 we describe a stable variant of the staircase algorithm for solving systems with tridiagonal and block tridiagonal matrices, also using the Fourier transform algorithm.

Keywords: Fast Fourier Transform; Discrete Fourier Transform; Arithmetic Operation; Fourier Coefficient; Grid Function (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-9272-8_4

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DOI: 10.1007/978-3-0348-9272-8_4

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