Abstract
We study the numerical solutions for modified Helmholz equation. Based on the potential theory, the problem can be converted into a boundary integral equation. Mechanical quadrature method (MQM) is presented for solving the equation, which possesses high accuracy order \(O(h_{max}^3)\) and low computing complexities. Moreover, the multivariate asymptotic error expansion of MQM accompanied with \(O(h_i^3)\) for all mesh widths \(h_i\) is got. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least \(O(h_{max}^5)\) by splitting extrapolation algorithm (SEA). The numerical examples support our theoretical analysis.
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