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These features, along with the manifestly compact nature of the fully node-based C1 finite elements, lead to minimum size matrices for an unconditionally stable method with order of accuracy h4.
It is seen in this work that the rise in accuracy of the full-discretization method with order continues to the proposed fourth order method where it (accuracy) peaks before a decline to the proposed fifth order method.
Then the cubic spline method with order of accuracy four for the differential equation (1) may be written as: U k + 1 − 2 U k + U k − 1 = h 2 12 η 2 f ― ― k + η + f ― ― k − η + 12 η 2 − 2 f ^ k + T k, 0 < η ≤ 1, k = 1 1 N Open image in new window (5).
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The CuMn-Al2O3 catalysts with different pores were synthesized by a co-impregnation method with ordered mesoporous Al2O3 as template.
PET images were reconstructed using an iterative method with ordered subset expectation maximization (2 iterations and 8 subsets) with a 5-mm filter.
In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure.
The Runge Kutta and Gauss Seidel methods obtain the second order accuracy, and the forward Euler method converges with order between one and two.
This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation.
Matlab implementation of two common fractional step projection methods is considered: the 2d Fourier pseudo-spectral method, and the 3d finite difference method with 2nd order spatial accuracy.
The optimized cumulant lattice Boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to Reynolds number 106.
There is still room for improvement in these PEE-based excellent works by using better prediction method with different order for different clips.
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