NEW HIGHLY ACCURATE STABLE SCHEMES FOR THE SOLUTION OF TELEGRAPHIC EQUATION WITH NEUMANN BOUNDARY CONDITIONS

In this paper, we present two new three level implicit schemes to solve telegraphic equation with Neumann boundary conditions. The accuracy of the proposed schemes is of ${ O(k^2 + k^2h^2 + h^4 ) }$ and ${O(k^4 + k^4h^2 ) }$, where ${ h > 0 }$ and ${ k > 0 }$ are the mesh sizes in the space and time directions respectively. The proposed schemes are shown to be solvable and unconditionally stable. Numerical experiments are presented to demonstrate the accuracy and efficiency of the new schemes.