Stronger than uniform convergence of multistep difference methods
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This paper is concerned with the numerical integration of ordinary differential equations of the orderx. Sufficient conditions and also necessary ones are given for the s-th difference quotient of the approximate solution to approach thes-th derivative of the exact solution fors >0. This requires a more subtle examination of the multiplicities of the characteristic roots of modulus 1.
KeywordsDifferential Equation Exact Solution Ordinary Differential Equation Approximate Solution Mathematical Method
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