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Smi7Ilia 2025-10-30 16:55:07 +01:00
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{\rtf1\ansi\ansicpg1252\cocoartf2709
\cocoatextscaling0\cocoaplatform0{\fonttbl\f0\fswiss\fcharset0 Helvetica;}
{\colortbl;\red255\green255\blue255;}
{\*\expandedcolortbl;;}
\paperw11900\paperh16840\margl1440\margr1440\vieww11520\viewh8400\viewkind0
\pard\tx566\tx1133\tx1700\tx2267\tx2834\tx3401\tx3968\tx4535\tx5102\tx5669\tx6236\tx6803\pardirnatural\partightenfactor0
\f0\fs24 \cf0 u(0)=0; u(1)=1;\
\
1) Heat equation in 1D: \
f(x)=-\uc0\u8706 (\u955 (x)\u8706 u/\u8706 x)/\u8706 x\
\
\pard\tx566\tx1133\tx1700\tx2267\tx2834\tx3401\tx3968\tx4535\tx5102\tx5669\tx6236\tx6803\pardirnatural\partightenfactor0
\cf0 2) f(x)=const=h; \uc0\u955 (x)=const=\u955 ;\
\
3) h= -\uc0\u955 *(\u8706 u^2)/\u8706 x^2\
\
4) The second derivative: h= -\uc0\u955 u\'94(x); \
\pard\tx566\tx1133\tx1700\tx2267\tx2834\tx3401\tx3968\tx4535\tx5102\tx5669\tx6236\tx6803\pardirnatural\partightenfactor0
\cf0 \
}