NUMERICAL SOLUTION OF NON-LINEAR COUPLED SYSTEM OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS BY θ- FINITE DIFFERENCE METHOD

Abstract

We constructed a θ-finite difference method to get the numerical solution for nonlinear couple system of hyperbolic partial differential equations. Von-Neumann  stability  analysis was  enforced  to  explain  the  stability of  the  present  method.   Toward  the  end,  one  illustrative  example  has  been introduced  to  comparing  the  numerical  and  exact  solutions  to  the  problem. The  results  obtained  indicate  that  the  proposed  method  is  very  effective  and highly accurate for such treatment problems.

Keywords: Numerical solution, Theta method, coupled system, Finite Difference, Hyperbolic equation, Nonlinear equation, initial condition, boundary condition, stability.