ThermoDynamics0pionium.tistory.com/attachment/cfile2.uf@99F731415A3E78... · Web viewdy dx -0.2xy=0...
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매매매 Matlab 매매매매매 매매매 매매매매매 Differential Equation 매매 매매매 Matlab 매 매매매매 매매매 매매매매매 Differential Equation 매 매매매매. 매매: OS – Windows 7 Ultimate K SP1 64bit MATLAB – R2016a (9.0.0341360) 64-bit 매매: n 매 매매 매매매매매매 Linear Ordinary Differential Equation (1) 1st-order Linear Homogeneous ODE (Non-autonomous) dy dx −0.2 xy =0 (2) 2nd-order Linear Homogeneous ODE (Autonomous) d 2 y dx 2 +2 dy dx +y=0 (3) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) d 2 y dx 2 +y=tan x (4) 3rd-order Linear Nonhomogeneous ODE (Non-autonomous) x 3 d 3 y dx 3 +2 x 2 d 2 y dx 2 −x dy dx +y=12 x 2 n 매 매매매 매매매매매매 Nonlinear Ordinary Differential Equation (1) 1st-order Nonlinear ODE – 매매매매매 2 매 매매매매 dy dx =2 xy 2 (2) 1st-order Nonlinear ODE – 매매매매매 매매 dy dx =xe y (3) 2nd-order Nonlinear ODE – 2 매 매매매매 매매매매 매 매매매매 매매매매 ( d 2 y dx 2 ) 2 =y 2 (4) 2nd-order Nonlinear ODE – 1 매 매매매매 매매매매 d 2 y dx 2 =2 x ( dy dx ) 2 (5) 2nd-order Nonlinear ODE – 2 매 매매매매 매매매매매 매매매매 매매 매 1 매 매매매 매매매매 y d 2 y dx 2 = ( dy dx ) 2 매매: 매매 매매매 매매매 m-file 매 매매매매 dsolve() 매매매 매매매매 매매
Transcript of ThermoDynamics0pionium.tistory.com/attachment/cfile2.uf@99F731415A3E78... · Web viewdy dx -0.2xy=0...
매트랩 Matlab 프로그램을 이용한 미분방정식 Differential Equation 풀이
매트랩 Matlab 을 이용하여 다양한 미분방정식 Differential Equation 을 풀어본다.
환경: OS – Windows 7 Ultimate K SP1 64bitMATLAB – R2016a (9.0.0341360) 64-bit
문제: n 계 선형 상미분방정식 Linear Ordinary Differential Equation(1) 1st-order Linear Homogeneous ODE (Non-autonomous)
dydx
−0.2xy=0
(2) 2nd-order Linear Homogeneous ODE (Autonomous)d2 ydx2
+2 dydx
+ y=0
(3) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous)d2 ydx2
+ y=tan x
(4) 3rd-order Linear Nonhomogeneous ODE (Non-autonomous)
x3 d3 ydx3
+2 x2 d2 ydx2
−x dydx
+ y=12 x2
n 계 비선형 상미분방정식 Nonlinear Ordinary Differential Equation(1) 1st-order Nonlinear ODE – 종속변수의 2 차 거듭제곱
dydx
=2x y2
(2) 1st-order Nonlinear ODE – 종속변수가 지수dydx
=xe y
(3) 2nd-order Nonlinear ODE – 2 계 도함수의 거듭제곱 및 종속변수 거듭제곱
( d2 ydx2 )2
= y2
(4) 2nd-order Nonlinear ODE – 1 계 도함수의 거듭제곱d2 ydx2
=2 x ( dydx )2
(5) 2nd-order Nonlinear ODE – 2 계 도함수의 계수함수에 종속변수 포함 및 1 계 도함수 거듭제곱
y d2 ydx2
=( dydx )2
풀이: 위의 문제를 매트랩 m-file 로 작성하여 dsolve() 함수를 이용하여 풀이
문제: n 계 초기값 문제 Initial Value Problem(1) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) IVP
x2 d2 ydx2
−5 x dydx
+8 y=8 x6
초기조건:
y ( 12 )=0y ' ( 12 )=0
(2) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) IVPd2 ydx2
+4 dydx
+4 y=(3+x ) e−2x
초기조건:y (0 )=2y ' (0 )=5
(3) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) IVPd2 ydx2
+ y=4 x+10sin x
초기조건:y (π )=0y ' ( π )=2
(4) 3rd-order Linear Homogeneous ODE (Autonomous) IVPd3 ydx3
+ dydx
=0
초기조건:y (π )=0y ' ( π )=2y ' ' (π )=−1
n 계 경계값 문제 Boundary Value Problem(1) 2nd-order Linear Homogeneous ODE (Autonomous) BVP
d2 ydx2
−2 dydx
+2 y=0
경계조건 1:y (0 )=0y ' ( π )=0
경계조건 2:y (0 )=1
y ( π2 )=1경계조건 3:
y (0 )=0y (π )=0
(2) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) BVP
x2 d2 ydx2
−5 x dydx
+8 y=24
경계조건 1:y (0 )=3
y (1 )=0경계조건 2:
y (1 )=3y (2 )=15
(3) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) BVPd2 ydx2
+3 y=6 x
경계조건:y (0 )=0
y (1 )+ y ' (1 )=0(4) 2nd-order Linear Nonhomogeneous ODE (Non-autonomous) BVP
d2 ydx2
+ y=x2+1
경계조건:y (0 )=5y (1 )=0
풀이: 위의 문제를 매트랩 m-file 로 작성하여 dsolve() 함수를 이용하여 풀이
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