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APPLICATIVE PROPERTIES OF SINUSOIDAL FOURIER SERIES EXPANSIONS OF MULTI-VARIABLE FUNCTIONS

Abstract : In our previous research [1, 2], we have developed a method of solving differential equations by determining the coefficients of the expansion of unknown functions in sinusoidal (or non-sinusoidal) series. This has proven to be an extremely powerful method, applicable to all types of differential (ODEs) and integrodifferential equations, linear and nonlinear, to systems of such equations, valid over a closed interval, regardless of their order and regardless of the complexity of their coefficients. The conditions required for the application of this method are not very restrictive and are easy to fulfill, in particular for the situations encountered in physics and in engineering. To apply this method also in the case of equations and systems of partial differential equations (for functions of several variables), it is necessary to generalize the applicatives formulas which describe the properties of monovariable functions (used in the case of ODEs) for functions depending on several variables (subject to partial differential equations PDEs), valid in a closed domain. As in the case of ODEs, the differentiation and the integration operations performed on the expansions in Fourier sinusoidal series (SFS) will turn into algebraic operations performed on the coefficients of the expansion. Therefore, solving PDEs will turn into solving some algebraic equations.
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https://hal.archives-ouvertes.fr/hal-03078881
Contributor : Török Arpad <>
Submitted on : Monday, February 22, 2021 - 1:13:33 PM
Last modification on : Monday, March 29, 2021 - 4:03:16 PM

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Arpad Török, Stoian Petrescu, Michel Feidt. APPLICATIVE PROPERTIES OF SINUSOIDAL FOURIER SERIES EXPANSIONS OF MULTI-VARIABLE FUNCTIONS. 2021. ⟨hal-03078881⟩

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