ACCURACY OF THE NUMERICAL SOLUTION OF A TWO-POINT BOUNDARY VALUE PROBLEM BY THE ORTHOGONAL COLLOCATION METHOD
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概要
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Accuracies of the numerical solution of a two-point boundary value problem by the orthogonal collocation method are examined. The collocation constants for first and second derivatives are calculated by the matrix operation method (Method 1) and the method based on Lagrange’s interpolation formula (Method 2). Comparison of the calculated results shows that Method 1 produces marked loss-of-significance errors with increasing number of collocation points, N. These values are used to solve the two-point boundary value problem concerning an immobilized enzyme reaction, and then to calculate the effectiveness factor. These numerical solutions are compared with those of the previously proposed method that provides a numerical solution whose accuracy is almost the same as machine accuracy. It is found that Method 1 provides a numerical solution of significantly low accuracy under the condition of steep concentration gradient and this is never improved, even if N is increased, while Method 2 gives highly accurate values by simply increasing N. These tendencies are shown to depend strongly on the accuracies of the collocation constants.
- 社団法人 化学工学会の論文
著者
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HASEGAWA Takahiro
Department of Anatomy and Cell Biology, Gunma University Graduate School of Medicine
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Hasegawa Takahiro
Department Of Systems Engineering Faculty Of Engineering Shizuoka University
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NAGASUE Hiroyuki
Department of Industrial Chemistry,Sasebo College of Technology
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SHIRAISHI Fumihide
Department of Biochemical Engineering and Science, Kyushu Institute of Technology
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Nagasue Hiroyuki
Department Of Biochemical Engineering And Science Kyushu Institute Of Technology
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Shiraishi F
Kyushu Inst. Technol. Iizuka Jpn
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Shiraishi Fumihide
Department Of Biochemical Engineering And Science Faculty Of Computer Science Adn Systems Engineerin
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