Transcription of Numerical Solution of Ordinary Differential Equations
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Numerical Solution of Ordinary Differential Equations
Numerical Solution of OrdinaryDifferential EquationsEndre S uliMathematical Institute, University of OxfordMarch 2, 20221 Contents1 Picard s theorem12 One-step Euler s method and its relatives: the -method .. Error analysis of the -method .. General explicit one-step method .. Runge Kutta methods .. absolute stability of Runge Kutta methods .. 193 linear multi-step Construction of linear multi-step methods .. Zero-stability .. Consistency .. Convergence .. Necessary conditions for convergence .. Sufficient conditions for convergence .. Maximum order of a zero-stable linear multi-step method .. absolute stability of linear multistep methods .. General methods for locating the interval of absolute stability.
Approximation of initial value problems for ordinary differential equations: one-step methods including the explicit and implicit Euler methods, the trapezium rule method, and Runge–Kutta methods. Linear multi-step methods: consistency, zero-stability and convergence; absolute stability. Predictor-corrector methods.
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