AN OPTIMAL NUMERICAL INTEGRATION METHOD OVER A LUNE BY USING AN EFFICIENT TRANSFORMATION TECHNIQUE
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초록
In this paper, we derive an optimal numerical integration method to integrate functions over a lunar model, a closed region bounded by two different circular boundaries. The region is discretized into two and suitable efficient transformations are used to transform the regions to a zeroone square. After the transformation, a product formula is applied to derive the proposed numerical integration method. The generalized Gaussian quadrature nodes and weights for one dimension are used in the derived integration formula for evaluating the results. The results obtained for seven different functions are tabulated along with a comparative study in order to show that the proposed method gives more accurate results using less number of quadrature points and is the optimal one.
Abstract
In this paper, we derive an optimal numerical integration method to integrate functions over a lunar model, a closed region bounded by two different circular boundaries. The region is discretized into two and suitable efficient transformations are used to transform the regions to a zeroone square. After the transformation, a product formula is applied to derive the proposed numerical integration method. The generalized Gaussian quadrature nodes and weights for one dimension are used in the derived integration formula for evaluating the results. The results obtained for seven different functions are tabulated along with a comparative study in order to show that the proposed method gives more accurate results using less number of quadrature points and is the optimal one.
참고문헌 (15)
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