The goal of treatment for spinal ependymoma is complete removal with minimal postoperative neurological deficit. The authors correlated the results of surgical management for spinal cord ependymoma with the rate of postoperative disease progression and the prognostic factors. Thirty-one cases of spinal ependymomas, surgically treated between 1979 and 1998, were retrospectively analyzed. The authors reviewed clinical features, radiological characteristics and operative findings for the surgical outcome analysis. Thirty-five percent of patients with preoperative Nurick's grade better than grade 4 showed improvement in functional status, whereas no improvement was observed in patients with preoperatively poorer functional status (P = 0.05). The proportion of complete surgical removals was influenced by tumor location (40% in cases around the conus versus 97% in other regions, P = 0.003) and histology (42% in the myxopapillary subtype versus 97% in the non-myxopapillary subtype, P = 0.001). Disease progression was observed in six cases, the mean progression free interval after surgical removal was 83 months and the 5-year progression free rate was 70%. Disease progression was found in two out of 23 cases from the complete removal group and in four out of eight cases from the incomplete removal group (P = 0.008). In the aspect of disease progression, the only statistically significant factor by multivariate analysis was the surgical extent of removal (P = 0.010). Of those patients where there was incomplete removal, radiation therapy lead to improved clinical results, which were not statistically significant (P = 0.27). In the surgical treatment of spinal cord ependymoma, preoperative functional status and the extent of removal were the significant prognostic factors influencing postoperative outcome. Early diagnosis is vital and complete removal of the tumor should be attempted in all surgical treatment of spinal ependymoma.

A second‐order splitting method is applied to a KdV‐like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well‐known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998

Finite element Galerkin approximate solutions for a KdV-like Rosenau equation which models the dynamics of dense discrete systems are cdnsidered. Existence and uniqueness of exact solutions are shown and the error estimates of the continuous time Galerkin solutions are discussed. For the fully discrete time Galerkin solutions, we consider the backward Euler method which results the first order convergence in the temporal direction. For the second order convergence in time, we consider a three-level backward method and the Crank-Nicolson method which give optimal convergence in the spatial direction.

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