  In this article, a numerical simulation of two dimensional nonlinear
sine-Gordon equation with Neumann boundary condition is obtained by using a
composite scheme referred to as a modified cubic B spline differential
quadrature method. The modified cubic B-spline serves as a basis function in
the differential quadrature method to compute the weighting coefficients. Thus,
the sine-Gordon equation is converted into a system of second order ordinary
differential equations (ODEs). We solve the resulting system of ODEs by an
optimal five stage and fourth-order strong stability preserving Runge Kutta
scheme. Both damped and undamped cases are considered for the numerical
simulation with Josephson current density function with value minus one. The
computed results are found to be in good agreement with the exact solutions and
other numerical results available in literature.
