CalcNum-14_2d-C-L4 - 02.11.2014 Quarta lista de exerccios C...

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02.11.2014 Quarta lista de exerc´ ıcios — C´ alculo Num´ erico / Turma C Depto. de Matem´ atica – UnB 1 – Sejam os m´ etodos de Euler, de Euler com valor intermedi´ ario e de Runge–Kutta de 2 a , 3 a e 4 a ordens. Para cada EDO de valor inicial abaixo, escolha aleatoriamente 2 dos m´ etodos acima e resolva a EDO calculando y ( x k ) y k := ?, com k := 10 passos. Coloque na tabela o valor correto da solu¸c˜ ao anal´ ıtica y ( x k ) e o erro real global E k := | y k - y ( x k ) | . Compare os 2 m´ etodos. (i) EDO y 0 = y x y (2) := 1 , com x R variando y (1) ? solu¸c˜ ao: y := x/ 2 (ii) EDO y 0 + y = x 2 - 3 x - 1 y (1) := 1 , com x R variando y (1 / 3) ? solu¸c˜ ao: y := e 1 - x + x 2 - 5 x + 4 (iii) EDO y 0 x = 2 y + x + 1 y (1 / 2) := - 1 / 2 , com x R variando y (2) ? solu¸c˜ ao: y := 2 x 2 - x - 1 / 2 (iv) EDO x e x - 1 = y 0 y y (1) := - 1 , com x R variando y (2) ? solu¸c˜ ao: y := - e (e x - 1)( x - 1) (v) EDO x = y 0 - y + cos x y (0) := - 1 , com x R variando y ( π/ 4) ? solu¸c˜ ao: y := cos x - sen x - e x 2 - x - 1 (vi) EDO y 0 = y + x + 2 x + 1 y (1) := - 3 , com x R variando y (0) ? solu¸c˜ ao: y := ( x + 1) ln | x +1 | 2 - 1 - 1 (vii) EDO y 0 = 2 y x + 1 + ( x + 1) 3 y (0) := 3 , com x R variando y (2) ?
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