ENTROPY SOLUTION OF A FIRST ORDER HYPERBOLIC TYPE EQUATIONS WITH A NON-CONVEX STATE FUNCTION IN A CLASS OF DISCONTINUOUS FUNCTIONS

Year 2012, Volume: 5 Issue: 1-2, 155 - 181, 06.05.2015

Mahir Resulov , Mahir Resulov , Ethem İlhan Şahin

Abstract

Makalede sabit katsayılı adi diferansiyel denklemler sistemi için yazılmış
Cauchy probleminin rezidü metodu ile gerçek çözümü elde edilmiş ve
söz konusu metot uygulanarak sabit gerilimli bir RC devre probleminin
çözümünün bulunması için uygulanmıştır.

Keywords

Riemann ve Buckley-Leverett problemleri, konveks olmayan durum fonksiyonu, konveks ve konkav katman, süresiz fonksiyonlar sınıfında sayısal çözüm

ENTROPY SOLUTION OF A FIRST ORDER HYPERBOLIC TYPE EQUATIONS WITH A NON-CONVEX STATE FUNCTION IN A CLASS OF DISCONTINUOUS FUNCTIONS

Abstract

In this paper, a method for obtaining an exact and numerical solution of the
Cauchy and first type initial boundary value problems for a first order partial
differential equation with a non convex state function is suggested. For this
purpose, we introduce an auxiliary problem since it has some advantages over
the main problem, and it is equivalent to the main problem in a definite sense.
Using this auxiliary problem, we propose a efficient method for finding the
location of shock which appears in the solution of main problem and its
evolution in time. The suggested auxiliary problem permit also us to prove
of convergence in mean of a numerical solution to the exact solution of the
main problem. Moreover, using the auxiliary problem we can write the higher
order numerical scheme with respect to the time variable. Some results of the
comparison of the exact and numerical solutions are illustrated. 

Keywords

Riemann's and Buckley-Leverett's problems, non-convex state function, convex and concave hull, numerical solution in a class of discontinuous functions