Numerical Solution of Tricomi Equation Using Theory of Symmetric Positive Differential Equations

Abstract

The Tricomi equation can be expressed in symmetric positive form. Admissiblee boundary conditions assure existence and uniqueness of solutions. In this paper it is shown what boundary conditions are admissible for the Tricomi equation for any region with piecewise smooth boundaries. A wide choice of boundary conditions is possible. A Tricomi equation with a known analytical solution is solved by a finite difference scheme for symmetric positive equations as an illustration of the numerical results which can be obtained. There is strong convergence to the analytical solutions, but pointwise divergence. Smoothing of the solution reduces the divergence, though, and satisfactory numerical results are obtained.