Extrapolation and Splitting Extrapolation Algorithm for Multidimensional Weakly Singular Integral of Product Type

In this paper, we use mid-rectangular quadrature rules to solve multidimensional weakly singular integrals of product type (MWSIP) and construct corresponding multi-step and multi-parameter asymptotic expansions of errors. The convergence order can turn from O(h
_i
^α
_i
⁺¹
) to O(h
₀
⁴
), -1 ≤ α
_i
≤ 0, h
₀
= max
_1≤i≤s
{h
_i
} by using extrapolation and splitting extrapolation algorithm. Moreover, we address a posterior error estimate and formulate self-adaptive algorithm. Numerical results illustrate that the method is of high accuracy and efficiency for solving MWSIP.