VISUALISATION OF CAUCHY PROBLEM SOLUTION FOR LINEAR T-HYPERBOLIC PDE

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