Titlebook: Numerical Methods for Ordinary Differential Equations; Initial Value Proble David F. Griffiths,Desmond J. Higham Textbook 2010 Springer-Ver

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Adaptive Step Size Selection, is proportional to 1/. and the accuracy of the results is proportional to .., for a method of order .. Thus, halving . is expected to double. the amount of computational effort while reducing the error by a factor of 2. (more than an extra digit of accuracy if . > 3).

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Modified Equations,ods. This attention is now shifted to the numerical method (primarily LMMs) and we ask whether the numerically computed values might be closer to the solution of a modified differential equation than they are to the solution of the original differential equation. At first sight this may appear to in

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,Geometric Integration Part II—Hamiltonian Dynamics,s. As in the previous chapter our emphasis is on.– showing that methods must be carefully chosen if they are to possess the correct geometric property, and.– using the idea of modified equations to explain the qualitative behaviour of numerical methods.

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Stochastic Differential Equations,imentally, in which case they are subject to measurement errors. Or the simulation of an epidemic might require an educated guess for the initial number of infected individuals. More fundamentally, there may be microscopic effects that (a) we are not able or willing to account for directly, but (b)

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1615-2085 in a first course, but also highlights new and emerging the.Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book fo

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