A New Single Step Full Discrete Scheme for a Semilinear Second Order Hyperbolic Equation
In this paper, we study a simplified single step full discrete scheme for a class of semilinear hyperbolic problems of second order. At first we obtain a system of second ordinary differential equations with initial value by use of spatially discrete finite element approximation with interpolated coefficients. Next in terms of a single step scheme to the time variable for this system we gain a fully discrete scheme with high accuracy. Finally we give the stable and convergence of the full discrete schemes.
K. Deng "A New Single Step Full Discrete Scheme for a Semilinear Second Order Hyperbolic Equation", Advanced Materials Research, Vols. 314-316, pp. 667-671, 2011