application of reproducing kernel hilbert space method for generalized 1-d linear telegraph equation

This paper presents a generalized 1-d linear telegraph equation. we have solved this equation by the reproducing kernel hilbert space (rkhs) method and compared it with other methods such as fourth-order compact difference and alternating direction implicit schemes and meshless local radial point interpolation (mlrpi). comparing the results of these three methods and comparing the exact solution, indicating the efficiency and validity of rkhs. the uniformly converges of the computed solution to the analytical solution are proved. note that the procedure is easy to implement, and it no need discretization, and is mesh-free too.