Numerical experiments with the Bratu equation in one, two and three dimensions
نویسندگان
چکیده
منابع مشابه
An Analytical and Numerical Study of the Two-Dimensional Bratu Equation
Bratu's problem, which is the nonlinear eigenvalue equation Au + 2 exp(u)= 0 with u = 0 on the walls of the unit square and 2 as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance of symmett:v: because of invariance under the C 4 rotation group and parity in both x and y, one can slash the size of the basis set by a...
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The Schrödinger equation for a point charge in the field of a stationary electric dipole admits bound states only when the dipole moment exceeds a certain critical value. It is not hard to see why this might be the case, but it is surprisingly difficult to calculate the critical dipole moment. The analogous problem should be simpler in one and two dimensions, but a general theorem forbids criti...
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An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...
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We generelize the Polyakov’s approach for Burgers turbulence in higher dimensions. In this respect, we write the operator product expansion and find the exact two–point functions of the Burgers equation in two and three–dimensions. We show that the angular dependence of the correlation functions satisfy the same equation, which is found in the instanton approach. PACS numbers 47.27.AK, 47.27.Jv
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ژورنال
عنوان ژورنال: Computational and Applied Mathematics
سال: 2013
ISSN: 0101-8205,1807-0302
DOI: 10.1007/s40314-013-0007-9