kontsyslos070109

kontsyslos070109 - DEAÖGA AEA ACAGA EGAYE5 79 Ód e ÐÐ u...

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Unformatted text preview: DEAÖGA AEA ACAGA EGAYE5 79 Ód e ÐÐ u t- Du xx = 0 , x > , t > u x (0 , t ) = 0 , t > u ( x, 0) = 1 Δ ( θ ( x- 1)- θ ( x- 1- Δ)) , x > d Ö u ( x, t ) aÒg eÖkÓÒeÒ ØÖa Ø iÓÒ eÒaÚ fÖgÑ Ò eØiÔÙÒk ØeÒ x Ú id Ø id eÒ t D eØhÓÑ Óg eÒaeÙ Ñ aÒÒÚ iÐÐkÓ ÖeØ Ðed eÖØ iÐÐeÒ jÑ Ò fÓ ÖØ×ØØÒ iÒgØ iÐÐh e Ða R aÚ u ÓhaÚb egÝÒÒ e Ð×eÚ iÐÐkÓ ÖeØia fÓ ÖÑ e Ð × idaÒÓhd eÒ iØ iÓÒ eÒaÚ fe ÐfÙÒk Ø iÓÒ eÒ × idaÒ4kaÒ Ðö ×Ò iÒg eÒ ×k Ö iÚa ××ÓÑ u ( x, t ) = 1 √ 4 πDt parenleftbiggintegraldisplay − 1 − 1 − Δ e − ( x − α ) 2 / 4 Dt 1 Δ dα + integraldisplay 1+Δ 1 e − ( x − α ) 2 / 4 Dt 1 Δ dα parenrightbigg = = 1 2Δ parenleftbigg erf x + 1 + Δ √ 4 Dt- erf x + 1 √ 4 Dt- erf x- 1- Δ √ 4 Dt + erf x- 1 √ 4 Dt parenrightbigg , d Ö x > , t > . D Δ → kÓÑÑ eÖb egÝÒÒ e Ð×eÚ Öd eØa ØØkÓÒÚ eÖg eÖaÑ Ó Ø δ ( x- 1) ÓhkÓÒeÒ ØÖa Ø iÓÒ eÒÑ...
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This note was uploaded on 10/07/2011 for the course FMA 021 taught by Professor Pellepettersson during the Spring '11 term at Lund.

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kontsyslos070109 - DEAÖGA AEA ACAGA EGAYE5 79 Ód e ÐÐ u...

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