| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Research Abstract |
The eigenvalue problem for differential operators is a basic problem in both engineering and mathematics. The upper bounds for the Laplacian have been given in history, but the lower bounds remain to be very difficult. In this research, a new algorithm is developed to give lower bounds for the eigenvalues of the Laplacian. Such an algorithm is based on the finite element method along with the use of the hypercircle equation. It is the first method that can easily deal with eigenvalue problems on domain of general shapes. The eigenvalue bounds are also successfully applied to solution verification for nonlinear partial differential equations defined on arbitrary polygonal domains.
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