Ordinary Differential Equations and Integral Equations, 6
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ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods). Problem Solving Environments? n th power of square matrices. chaotic behaviour. Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A -stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods. s stages. Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields. stiff and differential-algebraic systems. sensitivity analysis of solutions of DAE initial-value problems. error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect - the amount by which the approximation fails to satisfy the given equation and any side-conditions. stochastic differential equations has developed as a relatively new item of study in the area. differential equations with after-effect (retarded, delay, or neutral delay differential equations) and in this volume we include a number of papers on evolutionary problems in this area. Volterra and Fredholm-type integral equations. boundary-value problems for ordinary differential equation comprises eigenvalue problems such as Sturm-Liouville problems (SLP) and Schr�dinger equations. validated solutions of differential equations, that is, of computing guaranteed enclosures of solutions. h-, p- and hp- versions of the boundary element method, including pre-conditioning techniques.
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