Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order

Authors

  • H. Gunawan Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia.
  • E. Rusyaman Department of Mathematics, Padjajaran University, Bandung, Indonesia.
  • L. Ambarwati Department of Mathematics, State University of Jakarta, Jakarta, Indonesia

DOI:

https://doi.org/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)=cð‘–ð‘— , where 0<x1<...<xM,<1, 0<y1<...<yN<1, and cð‘–𑗠∈ â„ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented.

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