Numerical solution of the nonlinear evolutional inverse problem related to elastoplastic torsional problem


Tatar S., MURADOĞLU Z.

APPLICABLE ANALYSIS, vol.93, no.6, pp.1187-1200, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 93 Issue: 6
  • Publication Date: 2014
  • Doi Number: 10.1080/00036811.2013.823479
  • Title of Journal : APPLICABLE ANALYSIS
  • Page Numbers: pp.1187-1200

Abstract

This paper is devoted to the determination of an unknown function that describes elastoplastic properties of a bar under torsion. The mathematical (evolution) model leads to an inverse problem that consists of determining the unknown coefficient g = g(xi(2)), xi(2) = vertical bar del u vertical bar(2), in the nonlinear parabolic equation u(t) - del, (g(vertical bar del u vertical bar(2))del u) = 2t, (x,y,t) epsilon del(t)* := del x(0,t*], del subset of R-2 using measured output data given in the integral form. Existence of a quasi-solution of the considered inverse problem is obtained in the appropriate class of admissible coefficients. The direct problem is solved using a semi-implicit finite difference scheme. The inverse problem is solved using the semi-analytic inversion method (also known the fast algorithm). Finally, some examples are presented related to direct and inverse problems.