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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles

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3

Runge–Kutta methods

3.1  Gaussian quadrature

The exact solution of the trivial ordinary differential equation (ODE)

image

whose right-hand side is independent of image. Since a very rich theory and powerful methods exist to compute integrals numerically, it is only natural to wish to utilize them in the numerical solution of general ODEs

(3.1)

and this ...

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