Explicit Difference Methods for Solving the Cylindrical Heat Conduction Equation

? = 0(r = 0), i^=-F(i), (r=l) dr u dr where Fit) is an empirical function of t. In all cases, as far as the authors are aware, the differential coefficients in (1) are considered separately when replaced by differences, and the principal term in du the truncation error of any difference formula obtained in this way contains — and ö u —Z-. This can be seen by obtaining the time derivatives of u from (1) in the form ardu _ 1 du d u dt r dr âr2 ' â u __ 1 du 1 du 2d u d4u (2) W ~~ r*dr ~ r^dr2 r dr* dr1 ' d% = 9du _9_d% 4d% _3_d\ 3dju fu ât3 rb dr r4 dr2 r3 ¿V3 r2 âr4 r dr5 'dr6 '