Resolution of partial differential equations by rotation |
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Authors: | Hashem Mehrazin |
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Affiliation: | University of Tehran University, Faculty of Engineering, Civil Engineering Department, P.O. Box 11365-4563, Tehran, Iran |
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Abstract: | In this paper we study the rotation in R3 and we apply it to resolve some partial differential equations and the system of partial differential equations. For this, define first the rotation R(ψ,θ,φ) matrix and it's inverse and we prove that they are an orthogonal matrix. Then we calculate the eigenvalues of R(ψ,θ,φ) for different cases. Finally, for particular values of ψ, θ and φ, we apply the rotation to eliminate some partial derivatives in partial differential and system of partial differential equations to resolve them. |
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Keywords: | Partial differential equations Orthogonal matrices Matrix rotation Eigenvector |
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