On Numerical Computation of the Tricomi Equation

• Published in: Theoretical and Applied Mechanics Japan 2011/02/25, Vol.59, pp.359-372
• Main Authors: IMAI, Hitoshi, SAKAGUCHI, Hideo, ISO, Yuusuke
• Format: Article
• Language: English
• ISSN: 1348-0693; 1349-4244
• DOI: 10.11345/nctam.59.359

The Tricomi equation is solved numerically. Boundary value problems (BVPs) and ill-posed Cauchy problems (CPs) are considered. Problems are discretized by using the finite difference method (FDM) or the spectral collocation method (SCM). The numerical computation is carried out in the multiple-precision arithmetic. For BVPs both FDM and SCM work well. When the exact solution is a part of a global and analytic function accuracy of numerical results are expectable. They show that the maximum principle does not hold here. Some other BVPs are solved and numerical results are satisfactory. For CPs SCM works well but FDM does not. When the exact solution is a part of a global and analytic function accuracy of numerical results by SCM is expectable. Some other CPs are solved by SCM. Numerical results suggest that there exist some delicate problems as nonexsistence of the solution. They also show the effectiveness of SCM with the multiple-precision arithmetic in the numerical simulation for delicate problems.