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E. Rusyaman
Department of Mathematics, Padjajaran University, Bandung, Indonesia.
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order H. Gunawan; E. Rusyaman; L. Ambarwati
Journal of Mathematical and Fundamental Sciences Vol. 43 No. 3 (2011)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/itbj.sci.2011.43.3.6

Abstract

This paper presents a method of finding a continuous, real-valued, function of two variables z = u(x, y) defined on the square S := [0,1]2 , which minimizes an energy integral of fractional order, subject to the condition u(0, y) = u(1, y) = u(x,0) = u(x,1) = 0 and u(xi ,yj)=c𝑖𝑗 , where 0<x1<...<xM,<1, 0<y1<...<yN<1, and c𝑖𝑗 ∈ ℝ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented.
Co-Authors H. Gunawan L. Ambarwati