Numerical Solutions of Mildly Quasi-Linear Hyperbolic Equations and Generalizations

Finite difference methods for the numerical solution of one-space dimensional mildly quasi-linear hyperbolic equation with mixed derivative term, subject to appropriate initial and Dirichlet boundary conditions have been discussed. The methods are three level-implicit finite difference methods of order four. Linear stability analysis and fourth-order approximation at first time level for a one space dimensional quasi-linear hyperbolic equation with non zero second order time derivative term are discussed. The proposed method is generalized for a two and three space dimensional quasi-linear hyperbolic equation with a brief discussion of stability analysis. Numerical results are given to illustrate the accuracy of the proposed methods.