Numerical error patterns for a scheme with hermite interpolation for 1 + 1 linear wave equations

Numerical error patterns were presented when the fourth‐order scheme based on Hermite interpolation was used to solve the 1 + 1 linear wave equation. Since most non‐linear equations for real systems can be converted into linear forms by using proper transformations, this study certainly pertains its practical significance. The analytical solution was obtained under inhomogeneous initial and boundary conditions. It was found that not only the Hurst index of an error train at a given position but also its spatial distribution is dependent on the ratio of temporal to spatial intervals. The solution process with the fourth‐order scheme based on Hermite interpolation diverges as the ratio is greater than unity. The results show that regular error pattern and smaller maxima of absolute values of numerical errors can be obtained when the ratio is set as unity; while chaotic phenomena for the numerical error propagation process can appear when the ratio is less than unity. It was found that it is better to choose the ratio as unity for the numerical solution of 1 + 1 linear wave equation with the scheme; while other selections for the ratio in the scheme can bring about chaotic patterns for the numerical errors. Copyright © 2004 John Wiley & Sons, Ltd.