By Jacek Szarski

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Extra resources for Characteristics and Cauchy problem for nonlinear partial differential equations of first order

Example text

W e do so a n y w a y in t h e last e x a m p l e a b o v e t o p r o m o t e readability. T h e t e r n a r y o p e r a t o r is r i g h t - a s s o c i a t i v e w i t h r e s p e c t t o i t s first a n d t h i r d o p e r a n d s . A s o u r l a s t e x a m p l e , w e c o n s i d e r o p t i m i z a t i o n of a f u n c t i o n of o n e r e a l v a r i a b l e . T h e a l g o r i t h m m a y b e c a l l e d a " n o - d e r i v a t i v e line s e a r c h v i a s e c t i o n i n g , " o r t h e " g o l d e n s e a r c h .

L e t ' s c o n s i d e r a g a i n t h e e v a l u a t i o n of t h e i n t e g r a l / = t h e s i m p l e ( c r u d e ) v e r s i o n of S i m p s o n ' s R u l e : j T / ( x ) , ! 0; 10 11 χ += ( 4 . 0 * e x p ( - m i d * m i d ) ) ; 12 χ += e x p ( - b * b ) ; 13 χ *= ( ( b - a ) / 6 . 0 ) ; 14 15 r e t u r n 16 } x; / * end f u n c t i o n definition */ 20 d o u b l e S i m p s o n ( d o u b l e a , d o u b l e b ) ; /* prototype 21 d o u b l e a = 0 . 0 , b = 1 . 0 ; /* the endpoints */ */ 17 18 m a i n ( 19 ) { 22 23 p r i n t f ( " I n t e g r a l = y , l f \ n " , S i m p s o n ( a , b ) ) ; 24 } 2 3 .

X = 3 . 0 ; z . y = 4 . 0 ; 24 w . x = l . 0 ; w . y = 6 .

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Characteristics and Cauchy problem for nonlinear partial differential equations of first order by Jacek Szarski


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