Quick and dirty Maple worksheet to calculate truncation error of Crank-Nicolson scheme. Math/CS 6/72262 "Numer PDEs". C.G. (2-00) original version C.G. (5-07) .mw version Reset/clear. restart; Centered 1st-order time difference. vt := ( v(0,k/2) - v(0,-k/2) ) / k ;

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Taylor expand. 'vt' = mtaylor( vt, [ h, k ], 5 );

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Centered 2nd-order spatial difference. vxx := ( ( v(h, k/2) - 2*v(0, k/2) + v(-h, k/2)) / h^2 + ( v(h,-k/2) - 2*v(0,-k/2) + v(-h,-k/2)) / h^2 ) / 2 ;

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Taylor expand. 'vxx' = mtaylor( vxx, [ h, k ], 5 );

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Truncation error. mtaylor( vt - vxx, [ h, k ], 5 );

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