A novel approach for numerical computation of Burgers’ equation in (1+1) and (2+1) dimensions

An algorithm based on a new DQM with modified exponential cubic B-splines for solving hyperbolic telegraph equation in (2 + 1) dimension

In this paper, a new methodmodified exponential cubic B-Spline differential quadrature method(mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms ofL2andL∞error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes.