Stronger than uniform convergence of multistep difference methods
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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