Mathematics as a Tool by Johannes Lenhard & Martin Carrier

Author:Johannes Lenhard & Martin Carrier
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.You want to solve a system of differential equations x′(t) = f(x, t) with initial value x(t 0) = x 0 for the unknown x(t). The input data is the differential vector field f and the initial condition x 0, and the output is the solution vector x(t): x(t):

Even if it may seem a little pedantic, this notation makes clear the three possible ways of measuring error, as we will see shortly.

Now, when we use a computer for computations, we engineer the problem so that it can be implemented and efficiently executed on a digital computer. Thus, in our first example, instead of actually computing x = A −1 b, we would solve a modified problem that we could define as follows:

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