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°èÀÇ µ¿Àû °Åµ¿Àº Áß¿äÇÑ °ü½ÉÀÇ ´ë»óÀÌ´Ù. ¿ªÇÐÀû °è´Â À̵¿°Å¸®, ¼Óµµ, ±×¸®°í °¡¼Óµµ µîÀ» Æ÷ÇÔÇÏ°í ÀÖ´Ù. Àü±â ¶Ç´Â ÀüÀÚ°è´Â Àü¾Ð, Àü·ù ±×¸®°í À̵éÀÇ ½Ã°£ ÇÔ¼ö¸¦ Æ÷ÇÔÇÑ´Ù. ÀϹÝÀûÀ¸·Î, µ¿Àû ¼ºÁúÀ» ¹¦»çÇϱâ À§ÇØ »ç¿ëµÇ´Â ¹æÁ¤½ÄµéÀº À̵¿°Å¸®, Àü·ù¿Í ±×µéÀÇ ¹ÌºÐ Ç×µéÀ» ¹ÌÁöº¯¼ö·Î Æ÷ÇÔÇÏ°í ÀÖ´Ù. ¹ÌÁöÇÔ¼ö ÀÇ 1°è ¶Ç´Â ±× ÀÌ»óÀÇ »ó¹ÌºÐÇ×À» Æ÷ÇÔÇÏ°í ÀÖ´Â ¹æÁ¤½ÄÀº »ó¹ÌºÐ ¹æÁ¤½ÄÀ̶ó ºÒ¸®°í ¾à¾î·Î »ó¹Ì¹æ(ODE: Ordinary Differential Equation)À¸·Î ºÒ¸®±âµµ ÇÑ´Ù. ¹æÁ¤½Ä ÀÇ °è¼ö(order)´Â ÃÖ°íÂ÷ÀÇ µµÇÔ¼öÀÇ °è¼ö¿¡ ÀÇÇÏ¿© °áÁ¤µÈ´Ù. ¿¹¸¦ µé¾î, ¸¸ÀÏ 1°è µµÇÔ¼ö°¡ À¯ÀÏÇÑ ¹ÌºÐÇ×ÀÌ¸é ±× ¹æÁ¤½ÄÀº 1°è »ó¹Ì¹æÀÌ µÈ´Ù. ÇÑÆí, ÃÖ°íÂ÷ÀÇ µµÇÔ ¼ö°¡ 2°èÀÌ¸é ±× ¹æÁ¤½ÄÀº 2°è »ó¹Ì¹æÀ̶ó ºÒ¸®¿î´Ù. ÀÌ·¸°Ô ÇÏ¿© Àü±â ȸ·Î°è´Â º¸Åë 2°è »ó¹Ì¹æÀ¸·Î Ç¥ÇöµÇ´Âµ¥, ±×¸²¿¡ º¸À̴ ȸ·ÎÀÇ Àü·ù´Â ´ÙÀ½ ÀûºÐ-¹ÌºÐ¹æÁ¤½Ä ÀÇ Áö¹è¸¦ ¹Þ´Â´Ù.
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¿©±â¼ q(t)´Â ÃàÀü±â ÀüÇÏ(coulomb)ÀÌ´Ù. ½ºÀ§Ä¡´Â t=0¿¡¼ Æó¼âµÇ¾î ÀÖ´Ù°í °¡Á¤ÇÏ°í i=i(t)´Â Àü·ù ±×¸®°í »ó¼öµéÀº ´ÙÀ½°ú °°ÀÌ °áÁ¤µÈ´Ù.
R = 100¢¦10 (100, 50, 20, 10)¥Ø; L = 1.0e-8, 1.0e-7, 1.0e-6 H; C = 1.0e-8, 1.0e-7, 1.0e-6 F; E(t) = ¥ä(t) : impulse function;
Ãʱâ Á¶°ÇµéÀº q(0)=0 (ÃàÀü±âÀÇ Ãʱâ ÀüÇÏ) ÀÌ°í i(o)=0 ÀÌ´Ù. ¢Ñ½Ä (2)¸¦ ¹ÌºÐÇÏ¸é ´ÙÀ½°ú °°´Ù.
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¢Ñ½Ä (1)À» ´Ù½Ã ¾²¸é ´ÙÀ½°ú °°´Ù.
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»ó¹Ì¹æÀ» Ç®±â À§ÇÑ ¹®Á¦µéÀº, ÁÖ¾îÁø ¿µ¿ªÀÇ °æ°èÁ¡¿¡¼ Á¶°ÇµéÀÌ ¾î¶»°Ô Ç¥½ÃµÇ´Â°¡¿¡ µû¶ó ÃʱâÄ¡ ¹®Á¦ ¶Ç´Â °æ°èÄ¡ ¹®Á¦·Î ±¸ºÐµÇ¾î Áø´Ù. ÃʱâÄ¡ ¹®Á¦ÀÇ ¸ðµç Á¶°ÇµéÀº ¿µ¿ªÀÇ ½ÃÀÛÁ¡¿¡¼ Ç¥½ÃµÈ´Ù. ¹Ý´ë·Î Á¶°ÇµéÀÌ ¿µ¿ªÀÇ ½ÃÀÛÁ¡°ú Á¾°áÁ¡À¸·Î ³ª´©¾î¼ Á¤ ÀǵǸé ÀÌ ¹®Á¦´Â °æ°èÄ¡ ¹®Á¦°¡ µÈ´Ù. ÀϹÝÀûÀ¸·Î ½Ã°£¿µ¿ª¿¡¼ÀÇ »ó¹Ì¹æÀº ÃʱâÄ¡ ¹®Á¦À̸ç, µû¶ó¼ ¸ðµç Á¶°ÇµéÀº Ãʱ⠽ð£ÀÎ t=0¿¡¼ ÁÖ¾îÁø´Ù. ±×·¯¹Ç·Î ¿©±â¼ ¿ì¸®°¡ °í·ÁÇÏ´Â Àü±âȸ·Î°è´Â 2°è »ó¹Ì¹æÀÇ ÃʱâÄ¡ ¹®Á¦·Î±ÍÂøµÈ´Ù.
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»ó¹Ì¹æ¿¡¼ ÃÖ°í°èÀÇ µµÇÔ¼ö°¡ 2°è µµÇÔ¼öÀÏ ¶§, ÀÌ »ó¹Ì¹æÀº 2°è »ó¹Ì¹æÀ̶ó ºÒ¸®¿î´Ù. 2°è »ó¹Ì¹æÀº ´ÙÀ½°ú °°ÀÌ ÁÖ¾îÁø´Ù[ ½Ä (4) ÂüÁ¶].
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¿©±â¼ a, b¿Í s´Â »ó¼ö ¶Ç´Â t, u¿Í uÀÇ ÇÔ¼öÀÌ´Ù. ±×¸®°í µÎ ¹ø°¿Í ¼¼ ¹ø°ÀÇ ½ÄµéÀº Ãʱâ Á¶°ÇÀÌ µÈ´Ù. 2°è »ó¹Ì¹æÀº 2°ÔÀÇ Ãʱâ Á¶°ÇµéÀ» ÇÊ¿ä·Î Çϸç, ÀÌ´Â u(0)¿Í u(0)·Î ÁÖ¾îÁ® ÀÖ´Ù. ¸¸¾à a, b¿Í s°¡ u¿¡ ¹«°üÇÏ´Ù¸é, À§ ½ÄÀº ¼±Çü »ó¹Ì¹æÀÌ µÈ´Ù. ÀÌ·¸°Ô ÇÏ¿© Àü±âȸ·Î°è »ó¹Ì¹æÀº 2°è ¼±Çü »ó¹Ì¹æÀÌ µÈ´Ù. ¿© ±â¼´Â Àü¹æ Euler ¹ý¿¡ ÀÇÇÑ 2Â÷ »ó¹ÌºÐ ¹æÁ¤½ÄÀ» MATLABÀ» ÀÌ¿ëÇÏ¿© ¼öÄ¡ÀûÀ¸·Î °è»êÇÏ´Â ¹æ¹ýÀ» °£´ÜÈ÷ ¼Ò°³ÇÏ°í ÇØ´ç ÇÁ·Î±×·¥À» Á¦°øÇÑ´Ù. 4Â÷ Runge-Kutta ¹ýÀ» Àû¿ëÇÏ¿© MATLAB·Î ¼öÄ¡Çظ¦ ¾ò´Â º¸´Ù Á¤È®ÇÑ ¹æ¹ýÀº ´ÙÀ½Àý¿¡¼ ¼Ò°³Çϸç, º» ¿¬±¸¿¡¼´Â ÀÌ 4Â÷ Runge- Kutta ¹ýÀ¸·Î ¹ÌºÐ¹æÁ¤½ÄÀÇ ÃʱâÄ¡ ¹®Á¦¸¦ ÇØ°áÇϱâ·Î ÇÑ ´Ù.
Euler ¹ýÀ» Àû¿ëÇϱâ ÀüÀÇ Áß¿äÇÑ ´Ü°è´Â 2Â÷ »ó¹Ì¹æÀ» 1°è »ó¹Ì¹æÀÇ ½ÖÀ¸·Î ³ª´©´Â °ÍÀÌ´Ù. ´ÙÀ½°ú °°ÀÌ Á¤ÀÇÇÏÀÚ.
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±×¸®°í³ª¸é, ½Ä(7)Àº ´ÙÀ½°ú °°ÀÌ Ç¥Çö µÈ´Ù.
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¿©±â¼ »õ·Î¿î º¯¼öÀÎ vÀÇ Ç×À¸·Î ³ªÅ¸³»¾î¾ß ÇÏ´Â ÃʱâÁ¶°ÇÀº ½Ä (5)ÀÇ 2¹ø° ÃʱâÁ¶°ÇÀ¸·ÎºÎÅÍ µµÃâµÈ´Ù. ½Ä (5)´Â ÀÌÁ¦ µ¿Ä¡ÀÎ ´ÙÀ½°ú °°Àº ¿¬¸³ 1 °è »ó¹Ì¹æÀ¸·Î ³ªÅ¸³´Ù.
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MATLABÀ» Àû¿ëÇϱâ À§ÇÏ¿©, °¢ ½Ã°£´Ü°è µ¿¾ÈÀÇ °è»êÀº Çà·ÄÀÇ ÇüÅ·Π¾²¿©Áú ¼ö ÀÖ´Ù. ¿ì¼± y¿Í f¸¦ ´ÙÀ½°ú °°ÀÌ Á¤ÀÇÇÏÀÚ.
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±×·¯¸é ¹æÁ¤½Ä (6)Àº ´ÙÀ½°ú °°Àº ´ÜÀÏ ¹æÁ¤½ÄÀ¸·Î ¾²¿©Áø´Ù.
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À§ ½Ä¿¡ ÀÇÇØ Àü¹æÂ÷ºÐ ±Ù»ç¸¦ »ç¿ëÇÏ´Â Euler ½ÄÀº ´ÙÀ½°ú °°ÀÌ ÁÖ¾îÁø´Ù.
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¢Ñ¿ì¸®°¡ ÇØ°áÇØ¾ß ÇÒ ½Ä (4)¿¡ ´ëÇÑ ½Ä (8)ÀÇ Euler ¾Ë°í¸®ÁòÀ» ¾ò±â À§ÇØ º¤ÅÍÇüÀ¸·Î Ç¥ÇöÇÏ¸é ´ÙÀ½°ú °°´Ù.
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¢Ñ½Ä (8), (9), (10)À» ÀÌ¿ëÇÏ¿© MATLAB ½ºÅ©¸³Æ®¸¦ ÀÛ¼ºÇϸé, ´ÙÀ½°ú °°Àº ÇÁ·Î±×·¥À» ¾ò´Â´Ù.
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¡Û4Â÷ Runge-Kutta ¹æ¹ý
Euler ¹ýÀÇ ÁÖ¿äÇÑ °áÁ¡Àº Á¤È®µµ°¡ ³·´Ù´Â °ÍÀÌ´Ù. ³ôÀº Á¤È®µµ¸¦ ¾ò±â À§Çؼ´Â ½Ä (8)¿¡ ³ªÅ¸³ª´Â h°¡ ÀÛÀº °ªÀ̾î¾ß Çϴµ¥, ÀÌ·Î ÀÎÇÏ¿© °è»ê ¼Ò ¿ä½Ã°£ÀÌ ±æ¾îÁö°í ¹«½Ã ¸øÇÒ ¹Ý¿Ã¸²¿ÀÂ÷¸¦ À¯¹ßÇϱ⵵ ÇÑ´Ù. Runge- Kutta ¹æ¹ýÀº Euler ¹ýÀÇ ÀÌ·¯ÇÑ ºÎÁ¤ÀûÀÎ ¸éÀ» °³¼±Çϸç h°¡ °¨¼ÒÇÔ¿¡ µû¶ó ¿ÀÂ÷°¡ ´õ¿í »¡¸® °¨ ¼ÒÇϰԵǴ ÀåÁ¡À» °¡Áö°í ÀÖ´Ù. ´ÙÀ½ÀÇ »ó¹Ì¹æÀ» °í·ÁÇÏÀÚ
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¾Ë°í ÀÖ´Â ynÀÇ °ª¿¡ ´ëÇÏ¿© yn+1¸¦ °è»êÇϱâ À§ÇØ, ÀÇ ±¸°£¿¡¼ À§ ½ÄÀ» ÀûºÐÇÏ¸é ´ÙÀ½°ú °°´Ù.
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À§ ½Ä (12)ÀÇ ÀûºÐÀÇ ±Ù»ç°ªÀ» ±¸Çϱâ À§ÇØ, 2Â÷ Runge-Kutta¹ýÀº »ç´Ù¸®²Ã °ø½ÄÀ» ÀÌ¿ëÇϸç, 3Â÷ Runge-Kutta¹ýÀº ½ÉÇÁ½¼(Simpson)ÀÇ 1/3 ¹ýÄ¢À» ÀÌ ¿ëÇÑ´Ù. 4Â÷ Runge-Kutta¹ýÀº ½ÉÇÁ½¼(Simpson)ÀÇ 1/3 ¹ýÄ¢ ȤÀº 3/8 ¹ýÄ¢¿¡ ±âÃÊÇϸç, Å×ÀÏ·¯(Taylor) Àü°³ÀÇ 4Â÷Ç× ¸¸Å Á¤È®Çϱ⠶§¹®¿¡, ±¹ÁöÀû ¿ÀÂ÷´Â h5¿¡ ºñ·ÊÇÑ´Ù. ÇÑÆí, ½ÉÇÁ½¼ 1/3¹ýÄ¢¿¡ ±âÃÊÇÑ Ringe-Kutta ¹ýÀÇ ¾Ë°í¸®ÁòÀº ´ÙÀ½°ú °°ÀÌ ÁÖ¾îÁø´Ù.
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¢Ñ¿ì¸®°¡ °ü½ÉÀ» °¡Áø ½Ä (6)ÀÇ µÎ ¹æÁ¤½Ä ÁýÇÕ¿¡ ´ëÇÏ¿© 4Â÷ Runge-Kutta ¹ýÀ» Àû¿ëÇÏ¸é ´ÙÀ½°ú °°Àº ½ÄÀ» ¾ò´Â´Ù.
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À§ ½ÄÀ» º¤ÅÍÇüÀ¸·Î ³ªÅ¸³»¸é ´ÙÀ½°ú °°´Ù.
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À̷κÎÅÍ 4Â÷ Runge-Kutta ¹ýÀº ´ÙÀ½°ú °°ÀÌ ÁÖ¾îÁø´Ù.
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¢Ñ4Â÷ Runge-Kutta ¹ýÀ» ±¸ÇöÇϱâ À§ÇÑ MATLAB ½ºÅ©¸³Æ®(ÇÁ·Î±×·¥ ÆÄÀÏ)´Â À§ ½ÄÀ» »ç¿ëÇÏ¿© ÀÛ¼º °¡´ÉÇÏ´Ù. ½Ä (6)°ú ÇÔ²², À§ ½ÄÀ» Çà·Ä(matrix) Çü À¸·Î ³ªÅ¸³»¸é ´ÙÀ½°ú °°´Ù.
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(16)
±×¸®°í
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¢Ñ¿ì¸®°¡ ÇØ°áÇؾßÇÒ ½Ä (4)¿¡ 4Â÷ Runge-Kutta¹ýÀ» Àû¿ëÇÑ MATLABÀ» À§ÇÑ ¾Ë°í¸®ÁòÀ» ±¸ÇöÇÏÀÚ. ½Ä (16)À¸·ÎºÎÅÍ ´ÙÀ½½ÄÀ» ¾ò´Â´Ù.
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±×¸®°í ½Ä (17)À¸·ÎºÎÅÍ ´ÙÀ½ ¾Ë°í¸®ÁòÀ» ¾ò´Â´Ù.
(18)
¢Ñ¾Õ¼ Á¦½ÃµÈ Euler ¹ýÀÇ °Í°ú ´ëÀÀµÇ´Â Runge-Kutta¹ýÀÇ ÇÁ·Î±×·¥
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¡Ý¼öÄ¡°è»ê °á°úÀÇ Çؼ³
![](http://www.ground.co.kr/newsletter/20081120/d_0a.jpg) [±×¸² 0A] Euler Method: R = 100, L=2.0e-1, C = 1.0e- 5 X-axis, Y-axis : non-log scales
[ÇÁ·Î±×·¥ ¿¹1]ÀÇ ´ëÀÀ ±×·¡ÇÁ(Euler ¹ý)
![](http://www.ground.co.kr/newsletter/20081120/d_0b.jpg) [±×¸² 0B] Runge-Kutta Method: R=100, L=2.0e-1, C=1.0e- 5 X-axis, Y-axis : non-log scales
[ÇÁ·Î±×·¥ ¿¹ 1]ÀÇ ´ëÀÀ ±×·¡ÇÁ(4Â÷ Runge-Kutta¹ý), ÀÌÈÄ ¸ðµç ±×·¡ÇÁ´Â Runge-Kutta¹ý¿¡ ÀÇÇØ ¼öÄ¡ÀûÀ¸·Î °è»êÇÑ °á°úÀÌ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_1a.jpg) [±×¸² 1A] Runge-Kutta Method: L = 1.0e-8, C = 1.0e- 8 X-axis : log scale
X-ÃàÀº ½Ã°£(´ÜÀ§ ÃÊ)À» ³ªÅ¸³»°í log scaleÀÌ´Ù. L=1.0e-8H, C=1.0e-8F·Î °íÁ¤ÇÏ°í, R=10, 20, 50, 100¥ØÀÏ ¶§, I(t)¿Í Q(t) µéÀÇ 8°¡Áö ±×·¡ÇÁ¸¦ ³ª Ÿ³½´Ù. ¿©±â¼ Q(t)ÀÇ ±×·¡ÇÁ¿¡´Â ½ÇÁ¦º¸´Ù 1.0e7ÀÌ °öÇØÁ® ³ªÅ¸³ª ÀÖ´Ù. ±×¸²¿¡¼ º¸µíÀÌ I(t)´Â 0.1 ¥ìs¿¡¼ ¸¹ÀÌ °¨¼ÒÇØ ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_1b.jpg) [±×¸² 1B] Runge-Kutta Method: L = 1.0e-8, C = 1.0e- 8 X-axis : non-log scale
[±×¸² 1A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë ¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_2a.jpg) [±×¸² 2A] Runge-Kutta Method: L = 1.0e-7, C = 1.0e- 7 X-axis : log scale
X-ÃàÀº ½Ã°£À» ³ªÅ¸³»°í log scaleÀÌ´Ù. L=1.0e-7H, C=1.0e-7F·Î °íÁ¤ÇÏ°í, R=10, 20, 50, 100¥ØÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 8°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. ¿© ±â¼ Q(t)ÀÇ ±×·¡ÇÁ¿¡´Â ½ÇÁ¦º¸´Ù 1.0e6ÀÌ °öÇØÁ® ³ªÅ¸³ª ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_2b.jpg) [±×¸² 2B] Runge-Kutta Method: L = 1.0e-7, C = 1.0e- 7 X-axis : non-log scale
[±×¸² 2A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_3a.jpg) [±×¸² 3A] Runge-Kutta Method: L = 1.0e-6, C = 1.0e- 6, X-axis : log scale
X-ÃàÀº ½Ã°£À» ³ªÅ¸³»°í log scaleÀÌ´Ù. L=1.0e-6H, C=1.0e-6F·Î °íÁ¤ÇÏ°í, R=10, 20, 50, 100¥ØÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 8°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. ¿© ±â¼ Q(t)ÀÇ ±×·¡ÇÁ¿¡´Â ½ÇÁ¦º¸´Ù 1.0e6ÀÌ °öÇØÁ® ³ªÅ¸³ª ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_3b.jpg) [±×¸² 3B] Runge-Kutta Method: L = 1.0e-6, C = 1.0e- 6, X-axis : non-log scale
[±×¸² 3A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_4a.jpg) [±×¸² 4A] Runge-Kutta Method: R = 10, L = 1.0e-8 X- axis : log scale
R=10¥Ø, L=1.0e-8H·Î °íÁ¤ÇÏ°í, C=1.0e-8, 1.0e-7, 1.0e-6FÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 6°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. C°¡ Áõ°¡ÇÒ ¶§ I(t)¿Í Q(t)µµ µ¿½Ã¿¡ Áõ °¡ÇÔÀ» ¾Ë ¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_4b.jpg) [±×¸² 4B] Runge-Kutta Method: R = 10, L = 1.0e-8 X- axis : non-log scale
[±×¸² 4A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë ¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_5a.jpg) [±×¸² 5A] Runge-Kutta Method: R = 10, L = 1.0e-7 X- axis : log scale
R=10¥Ø, L=1.0e-7H·Î °íÁ¤ÇÏ°í, C=1.0e-8, 1.0e-7, 1.0e-6FÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 6°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. C°¡ Áõ°¡ÇÒ ¶§ I(t)¿Í Q(t)µµ µ¿½Ã¿¡ Áõ °¡ÇÔÀ» ¾Ë ¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_5b.jpg) [±×¸² 5B] Runge-Kutta Method: R = 10, L = 1.0e-7 X- axis : non-log scale
[±×¸² 5A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_6a.jpg) [±×¸² 6A] Runge-Kutta Method: R = 10, L = 1.0e-6 X- axis : log scale
R=10¥Ø, L=1.0e-6H·Î °íÁ¤ÇÏ°í, C=1.0e-8, 1.0e-7, 1.0e-6FÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 6°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. C°¡ Áõ°¡ÇÒ ¶§ I(t)¿Í Q(t)µµ µ¿½Ã¿¡ Áõ °¡ÇÔÀ» ¾Ë ¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_6b.jpg) [±×¸² 6B] Runge-Kutta Method: R = 10, L = 1.0e-6 X- axis : non-log scale
[±×¸² 6A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë ¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_7a.jpg) [±×¸² 7A] Runge-Kutta Method: R = 20, C = 1.0e-8 X- axis, Y-axis : log scales
R=20¥Ø, C=1.0e-8F·Î °íÁ¤ÇÏ°í, L=1.0e-8, 1.0e-7, 1.0e-6HÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 6°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. LÀÌ Áõ°¡ÇÒ ¶§ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ ÇÏ°í Àû´çÇÑ ½Ã°£(0.1 ¥ìs)¿¡¼ ±× Áõ°¡ÆøÀÌ µÐÈ µÈ´Ù. ÀÌ·Î ÀÎÇØ I(t)°¡ Áõ°¡ÈÄ °¨¼ÒÇÏ°Ô µÈ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_7b.jpg) [±×¸² 7B] Runge-Kutta Method: R = 20, C = 1.0e-8 X- axis: non-log scale, Y-axis: log scale
[±×¸² 7A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_8a.jpg) [±×¸² 8A] Runge-Kutta Method: R = 20, C = 1.0e-7 X- axis, Y-axis : log scales
R=20¥Ø, C=1.0e-7F·Î °íÁ¤ÇÏ°í, L=1.0e-8, 1.0e-7, 1.0e-6HÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 6°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. LÀÌ Áõ°¡ÇÒ ¶§ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ ÇÏ°í Àû´çÇÑ ½Ã°£(0.1 ¥ìs)¿¡¼ ±× Áõ°¡ÆøÀÌ µÐÈ µÈ´Ù. ÀÌ·Î ÀÎÇØ I(t)°¡ Áõ°¡ÈÄ °¨¼ÒÇÏ°Ô µÈ´Ù. ±×·¯³ª ¿©±â¼´Â [±×¸² 7A]º¸´Ù º¹·ÏÇÑ Á¤µµ°¡ µÐÇÏ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_8b.jpg) [±×¸² 8B] Runge-Kutta Method: R = 20, C = 1.0e-7 X- axis: non-log scale, Y-axis: log scale
[±×¸² 7A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_9a.jpg) [±×¸² 9A] Runge-Kutta Method: R = 20, C = 1.0e-6 X- axis, Y-axis : log scales
R=20¥Ø, C=1.0e-6F·Î °íÁ¤ÇÏ°í, L=1.0e-8, 1.0e-7, 1.0e-6HÀÏ ¶§, I(t)¿Í Q(t)µéÀÇ 6°¡Áö ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. LÀÌ Áõ°¡ÇÒ ¶§ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ ÇÏ°í Àû´çÇÑ ½Ã°£(0.1 ¥ìs)¿¡¼ ±× Áõ°¡ÆøÀÌ µÐÈ µÈ´Ù. ÀÌ·Î ÀÎÇØ I(t)°¡ Áõ°¡ÈÄ °¨¼ÒÇÏ°Ô µÈ´Ù. ±×·¯³ª ¿©±â¼´Â [±×¸² 8A]º¸´Ù º¹·ÏÇÑ Á¤µµ°¡ µÐÇÏ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_9b.jpg) [±×¸² 9B] Runge-Kutta Method: R = 20, C = 1.0e-6 X- axis: non-log scale, Y-axis: log scale
[±×¸² 9A]¿Í °°Àº Á¶°Ç¿¡¼ I(t)¿Í Q(t)¸¦ ³ªÅ¸³»´Âµ¥, ¿©±â¼´Â X-ÃàÀÌ log scaleÀÌ ¾Æ´Ï´Ù. ±×·¡ÇÁ¿¡¼ º¸µíÀÌ Q(t)´Â Áö¼öÀûÀ¸·Î Áõ°¡ÇÏ°í ÀÖÀ½À» ¾Ë¼ö ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_10a.jpg) [±×¸² 10A] Q0*exp[-t/(RC)] : R = 100, 50, 10, C = 1.0e- 8 X-axis : non-log, Y-axis : log scale
C=1.0e-8F·Î °íÁ¤ÇÏ°í, ±×·¡ÇÁÀÇ ³ôÀÌ¿¡ ´ëÀÀÇÏ¿©, Â÷·Ê·Î R=10, 50, 100¥ØÀÏ ¶§ Áö¼öÇÔ¼ö Q(t)=Q0exp[-1/(RC)]ÀÇ ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. Y- ÃàÀº log scale·Î ³ªÅ¸³»°í ÀÖ´Ù.
![](http://www.ground.co.kr/newsletter/20081120/d_10b.jpg) [±×¸² 10B] Q0*exp[-t/(RC)] : R = 100, 50, 10, C = 1.0e- 7 X-axis : non-log, Y-axis : log scale
C=1.0e-7F·Î °íÁ¤ÇÏ°í, ±×·¡ÇÁÀÇ ³ôÀÌ¿¡ ´ëÀÀÇÏ¿©, Â÷·Ê·Î R=10, 50, 100¥ØÀÏ ¶§ Áö¼öÇÔ¼ö Q(t)=Q0exp[-1/(RC)]ÀÇ ±×·¡ÇÁ¸¦ ³ªÅ¸³½´Ù. Y- ÃàÀº log scale·Î ³ªÅ¸³»°í ÀÖ´Ù.
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¡ÛR °ªÀº ³·À»¼ö·Ï ¹æÀü½Ã°£( 0.15 §Á(¹ÝÄ¡Æø ±âÁØ))ÀÌ »¡¶óÁö°í L=1¡¿10-8 H, C=1¡¿10-8 FÀÏ °æ¿ì R¢¦5 §Ù(ÀÓÇÇ´ø½º)À̸é, ³«·Ú³ª ¼Áö, Noise, ÀÌ»ó Àü¾ÐÀÌ ¹ß»ýµÈ´ÙÇÏ¿©µµ Àåºñ º¸È£¿¡ ¹®Á¦°¡ ¾øÀ» °ÍÀ¸·Î ¼öÄ¡Çؼ® °á°ú°¡ ³ª¿Â´Ù. |