VISUALISATION OF CAUCHY PROBLEM SOLUTION FOR LINEAR T-HYPERBOLIC PDE

Year 2016, Volume: 4 Issue: 1, 193 - 202, 01.04.2016

Oğuzer Sinan Ayşe Bulgak

Abstract

Graphics Constructor and Cauchy Solver computer dialogue pro- grams were created by A.Bulgak and D.Eminov [1, 2]. These programs use the one dimensional spline functions for visualisation of graphics of real func- tions. The study generalises this approach to the Cauchy problem for linear one dimensional t-hyperbolic PDE[4, 5, 7].

Keywords

cubic spline, two dimensional splines, Cauchy problem, t-hyperbolic equations

References

• [1] A.Bulgak and D.Eminov, Graphics Constructor2.0, Selcuk Journ. Appl. Math., Vol:4, No.1 (2003), 42-57.
• [2] A. Bulgak and D. Eminov, Cauchy Solver, Selcuk Journ. Appl. Math., Vol:4, No.2 (2003), 13-22.
• [3] Rogers D.F, Adams J.A., Mathematical Elements for Computer Graphics McGraw-Hill Pub- lishing, New York, 1990.
• [4] Godunov S.K., Zabrodin A.B., Ivanov M.Ya., Kraiko A. N., Numerical Solving Many- Dimensional Problems of Gas Dynamics, Nauka, Moscow(Russian), 1976.
• [5] Godunov S.K.,Equations of Mathematical Physics, 2nd Edition, Nauka, Moscow(Russian), 1979.
• [6] H. Bulgak and D.Eminov,Computer dialogue system MVC, Selcuk Journ. Appl. Math., Vol:2, No.2 (2001), 17-38.
• [7] O.Sinan, Two Dimensional Spline Functions, PhD thesis in Math., Selcuk Universty, 2008, Konya, Turkey.