Computational Complexity of Initial Value Problems (draft)
نویسنده
چکیده
h.0/ D 0; h.t/ D g t; h.t/ ; t 2 Œ0; 1 (1) in h W Œ0; 1 ! R (Figure 1). A simple sufficient condition that guarantees unique existence of solution h is that g be Lipschitz continuous (along its second argument), which is to say, jg.t;y0/ g.t;y1/j L jy0 y1j; t 2 Œ0; 1; y0;y1 2 R (2) for some constant L independent of y0, y1 and t [16]. We are interested in the computational complexity of the (unique) solution h under this condition.
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