Solving One-dimensional Hyperbolic Telegraph Equation Using Cubic B-spline Quasi-interpolation

Abstract

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme. Keywords—Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.