Numerical integration method for triple integrals using the second kind Chebyshev wavelets and Gauss-Legendre quadrature

作者：Zhou, Fengying^*; Xu, Xiaoyong; Zhang, Xijing

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37(3): 3027-3052.

DOI：10.1007/s40314-017-0494-1

• The second kind Chebyshev wavelet
• Gauss-Legendre quadrature
• Numerical integration
• Triple integral
• Jacobian determinant

In this paper, a computational method combining the second kind Chebyshev wavelets and Gauss-Legendre quadrature is proposed for numerical integrations of arbitrary functions over regions like cuboid, tetrahedron, cylinder, cone, paraboloid and ellipsoid. Gauss-Legendre quadrature is used to convert a triple integral into a double integral and integral regions are transformed to the standard integration region by linear and nonlinear transformation. Moreover, convergence and accuracy estimation of the second kind Chebyshev wavelets expansion of two dimensions is given. Illustrative examples have been demonstrated to show the applicability and accuracy of the present method.

• 出版日期2018-7
• 单位东华理工大学