Numerical solution of wave equation using higher order methods

The paper deals with the numerical solution of partial differential equations. The one-dimensional wave equation was chosen for experiments; it is solved using Method of Lines which transforms the partial differential equation into the system of ordinary differential equations. The solution in time remains continuous, and the Modern Taylor Series Method is used for solving the system of initial value problems. On the other hand, the spatial discretization is performed using higher order finite difference formulas, which can be unstable. The necessity of the variable precision arithmetic to stabilize the solution is discussed in this paper. The seven point difference formula is analysed as an example of higher order finite difference formulas.