NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM BY COMBINED TAYLOR SERIES METHOD WITH A TECHNIQUE FOR RAPIDLY SELECTING SUITABLE STEP SIZES
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概要
- 論文の詳細を見る
A novel numerical method, based on the combined Taylor series method with a technique for rapidly selecting suitable step sizes, is given for solving two-point boundary value problems. The differential equation for an immobilized enzyme reaction is considered as a model system. Comparisons between numerical and exact solutions for the first-order reaction show that the proposed method promises superhigh-order accuracy that is almost the same as machine accuracy over wide ranges of relevant parameters. The final value of the increment or decrement used to obtain a new estimate in the Newton-Raphson iterative scheme is found to be approximately the same as the relative error of the calculated value, which means that this final value is useful to predict the accuracy of a numerical solution of the differential equation that does not provide an analytical solution. Moreover, it is shown that the selected stepsizes are suitable values that cause little loss-of-significance errors.
- 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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