Some remarks on a class of rational approximations to the cosine

Some previously introduced methods for the numerical solution of second-order evolution equations based on a class of rational approximations to the cosy, y real, with denominators (1+x²y²)^s are revisited. It is shown that maximal accuracy occurs for each integers1 for a suitable choice of the parameterx. An improved sufficient condition for unconditional stability is obtained. Conditional stability and periodicity of these methods are also studied.Work supported by USARO Grant DAAG 29-78-C-0024.