MACM 316 Lecture 17: MACM316- Part 6.4 Numerical Solutions of Differential Equations
15 Oct 2018
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Macm 316-part 6. 4: numerical solution of di erential equations. So far, we"ve assumed that the step-size h in our methods is constant. However, it makes sense that we may have parts of our problem were a smaller h is more appropriate (e. g. a region of rapid change), and areas where a large h is acceptable (areas where our solution is at) As with an adaptive quadrature rule, we want to be able to specify: function f (t, y, error tolerance tol, initial conditions for our problem. And receive a solution where the global error , |wi yi| < tol for all i = 0n . However, this is more complicated than for quadrature. Much like for numerical integration, practical numerical methods for. Ivps usually pick the stepsize adaptively to ensure a good tradeo between accuracy and e ciency. Consider a pth order method- for example, a runge-kutta method. 1 w0 = wi+1 = wi + h (ti, wi, h)
