1991 Fiscal Year Final Research Report Summary
Research and Development of Numerical Analysis Software
| Project/Area Number |
02640173
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hiroshima University |
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Principal Investigator |
SHINTANI H. Hiroshima Univ. Fac. of School. Education, Prof., 学校教育学部, 教授 (90033802)
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| Co-Investigator(Kenkyū-buntansha) |
KAGEYAMA S. Hiroshima Univ. Fac. of School Education, Ass. Prof., 学校教育学部, 助教授 (70033892)
IKEDA A. Hiroshima Univ. Fac. of School Education, Ass. Prof., 学校教育学部, 助教授 (30093363)
OKADA Y. Hiroshima Univ. Fac. of School Education, Prof., 学校教育学部, 教授 (70093739)
ISHIBASHI Y. Hiroshima Univ. Fac. of School Education, Prof., 学校教育学部, 教授 (30033848)
YAMAGUTI K. Hiroshima Univ. Fac. of School Education, Prof., 学校教育学部, 教授 (20040090)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Numerical analysis software / Numerical methods for differential equation / Numerical methods for algebraic equations / Mathematics education software |
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| Research Abstract |
Methods for numerical solution of initial value problem for systems of stiff ordinary differential equations are studied. Existence of 5-stage singley diagonally implicit one-step methods of order 5 is proved. Starters for numerical solution methods are obtained for a singular systems of differential equations of the second order. It has been shown that there exist two-step methods of order 4, 5 and 6 which enable us to estimate the local error and to interpolate at nonstep points and that there exist such methods with one off-step point of order 5, 6 and 7.
The behavior of solution curves of nonlinear systems in the neighborhood of a nonsimple bifurcation point is studied in detail. Methods for constructing extended systems to determine double and triple turning points are developed.
Characterization of semi-regular and regular experimental designs is given and nonexistence of a certain kind of design is proved.
A personal computer program is written for diagnosing the ability of adding two integers of two figures.
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