MACM 316 Lecture 15: MACM316- Part 6.2 Numerical Solutions of Differential Equations
15 Oct 2018
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Macm 316-part 6. 2: numerical solution of di erential equations. A system of odes has the form, for a t b dy1 dt dy2 dt dyn dt. The corresponding ivp is given the initial conditions y1(a) = 1, y2(a) = 2. As in the case where d = 1, our aim is to nd the functions y1(t), y2(t), , yd(t). It makes sense to use vector notation here. De ne the vector func- tions y(t) = y1(t) y2(t) yd(t) f (t, y) = f1(t, y1) f2(t, y2) fd(t, yd) 1 y (t) = f (t, y), a t b, y(a) = (2) where. Note that y (t) is the vector deriva- tive , i. e. y (t) = y . Applying a numerical method such as euler"s to the system (2) is very similar to the 1d case. We let w0 = wi+1 = wi + hf (ti, wi i = 0, 1, , n where wi y(ti).
