Abstract
In this paper, by using a quartic spline in space and generalized trapezoidal formula in time direction, one-dimensional telegraphic equations are solved. We present new classes of two-level schemes. The accuracy of these methods are O ( k 2 + h 4 ) . It has been shown that by suitably choosing parameter, a high accuracy scheme of O ( k 3 + h 4 ) can be derived from our methods. Numerical results demonstrate the superiority of the new scheme.
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