計(jì)算方法第八章ppt課件-資料下載頁(yè)
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【正文】 )22( , )nnnnnnnnnny y K K K KK hf x yKhK hf x yKhK hf x yK hf x h y K??? ? ? ? ???????? ? ????? ? ???? ? ? ??寫成分量形式： , 1 , 1 2 3 41 1 2111 212 1 2212 223 1 24 1 13 2 23 31( 2 2 )6( , , , , )( , , , , )2 2 2 2( , , , , )2 2 2 2( , , , , )1 , 2 , ,i n i n i i i ii i n n n m nmi i n n n m nmi i n n n m ni i n n n m n my y K K K KK hf x y y yKKKhK hf x y y yKKKhK hf x y y yK hf x h y K y K y Kim??? ? ? ? ???? ? ? ? ??? ? ? ? ?? ? ? ? ??????????????例子： 1 1 22212( 0 1 )( 0 ) 0 , ( 0 ) 1y y yy y xyy? ? ? ???? ? ? ? ??? ???1 , 1 1 , 11 1213 1411 1 211 2112 1 212 2213 1 214 1 13 2 231(262)()[ ( ) ]22[ ( ) ]22[ ( ) ]nnnnnnnnnny y K KKKK h y yKKK h y yKKK h y yK h y K y K??? ? ???????? ? ????? ? ? ? ????? ? ? ? ???? ? ? ? ???2 , 1 2 , 21 2223 2421 22122 22223 224 2 231(262)()2()2()nnnnnny y K KKKK hyKK h yKK h yK h y K??? ? ????????????? ? ????? ? ???? ? ??? DOUBLE PRECISION h,y1(0:100),y2(0:100) double precision ak1,ak2,ak3,ak4,bk1,bk2,bk3,bk4 OPEN(20,FILE=39。39。,STATUS=UNKNOWN) h= y1(0)= y2(0)= do 10 i=1,10 ak1=h*(y1(i1)+y2(i1)) bk1=h*y2(i1) ak2=h*((y1(i1)+ak1/)+y2(i1)+bk1/) bk2=h*(y2(i1)+bk1/) ak3=h*((y1(i1)+ak2/)+y2(i1)+bk2/) bk3=h*(y2(i1)+bk2/) ak4=h*((y1(i1)+ak3)+y2(i1)+bk3) bk4=h*(y2(i1)+bk3) y1(i)=y1(i1)+(ak1+2*ak2+2*ak3+ak4)/ y2(i)=y2(i1)+(bk1+2*bk2+2*bk3+bk4)/ 10 continue do 20 i=0,10 write(20,100) i*h,y1(i),i*h*exp(i*h),y2(i),exp(i*h) 100 format (1x,,) 20 continue END 取 h= 節(jié)點(diǎn) y1精確 y1數(shù)值 y2精確 y2數(shù)值 .00 .00000 .00000 .10 .09048 .09048 .90484 .90484 .20 .16375 .16375 .81873 .81873 .30 .22224 .22225 .74082 .74082 .40 .26813 .26813 .67032 .67032 .50 .30326 .30327 .60653 .60653 .60 .32929 .32929 .54881 .54881 .70 .34761 .34761 .49659 .49659 .80 .35946 .35946 .44933 .44933 .90 .36591 .36591 .40657 .40657 .36788 .36788 .36788 .36788 高階微分方程可以轉(zhuǎn)換為一階方程組進(jìn)行求解。 令： ( ) ( 1 )0 1 ( 1 ) 10 0 0 0 0 0( , , , , , )( ) , ( ) , , ( )nnnny f x y y y yy x y y x y y x y???? ????? ? ?( 1 )0 1 1( ) ( ) , ( ) ( ) , , ( ) ( )n ny x y x y x y x y x y x? ??? ? ?01121 0 1 2 10 0 00 0 0 1 0 1 1 0 1( ) ( )( ) ( )( ) ( , ( ) , ( ) , ( ) , , ( ) )( ) , ( ) , , ( )nnnny x y xy x y xy x f x y x y x y x y xy x y y x y y x y?????? ??? ???? ??? ??? ? ? ??
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