Error analysis and novel near-field preconditioning techniques for Taylor series multipole-BEM[J] . Zejun Chen,Hong Xiao,Xia Yang.Engineering Analysis with Boundary Elements . 2009 (2)Chen Zejun,Xiao Hong,Yang Xia.Error analysis and novel near-field preconditioning techniques for Taylor series ...
whileS 0 (2n)andI 0 (2n)arecomputedusingTaylorseries. Whenallseriesareevaluatedusingthebinarysplittingtechnique(see[4,§4.9]), thefirstddigitsofγcanbecomputedinessentiallyoptimaltimeO(d 1+ε ). ∗ MathematicalSciencesInstitute,AustralianNationalUniversity,Canberra,Australia [gamma@rpbrent];supportedby...
写切线,用欧拉方法(Euler's method),解微分方程,是老三样。 7.无穷级数的题,肯定会涉及到已知某个函数的泰勒级数(Taylor series),写出另外一个相关联的函数的泰勒级数。 今年大概率还是有交错级数(alternating series)的误差边界(error bound),也可能出现拉格朗日误差边界(Lagrange error bound)。大概率还是会让计算i...
Using Taylor expansion of Δu, we have Δu(jh)=Δu(z)+(jh−z)Δu′(z)+12(jh−z)2Δu″(z) Since Δu(jh)=0 and Δu'(z)=0, we obtain (7.14)|Δu(z)|=|12(jh−z)2Δu″(z)|≤18h2max|u″| The above results are applied to the following equation. (7.15)0≤‖...
Central finite difference stencils can easily be constructed on the grid points away from the boundaries by using Taylor expansion. On the few grid points close to the boundaries, one-sided stencils are used as boundary closure. The boundary closure can be specially constructed so that the finite...
error estimate is based on the numerical experiments. This is because the conventional Taylor series expansion for error estimate used in the finite difference scheme is not applicable in the RBF approximation. At this time, the theoretical error analysis for derivative approximation ...
The Leibniz rule, sometimes referred to as the Leibniz's rule for differentiation, is an useful method for differentiating integrals where the limits are functions. Assume {eq}\displaystyle F(x) = \int_{a(x)}^{b(x)} f(t)...
Earlier, Alon and Lubetzky (2006) showed that the series of independence numbers of strong powers of a fixed graph can exhibit a complex and unpredictable structure. In this article, we propose polynomial algorithms that approximate the capacity for some channels....
Moreover it yields some remarkable advantages as compared with other methods, in particular, with the series expansion method that has recently received considerable attention. Expressions for the truncation error are also given and their derivation is reported in the Appendix. Finally, examples of ...
1). We explore this broader mitigation potential with a series of numerical experiments below, wherein we simulate noisy Trotter circuits for systems of interacting fermions and spin-1/2 particles, respectively. Subsystem-symmetrized Pauli shadows While random Pauli measurements are efficient for ...