In order to solve the integral approximation problem,using second derivative,a numerical integral formula is constructed by three points with six conditions,the formula was verified with 7degree algebraic precision.Then,extend it to the compound formula and improved formula.For each formula the remainde...
What is the second derivative formula? The second derivative formula is the same as that for the first derivative only f(x) is replaced by f'(x). Making this substitution yields: f(x) = (f'(x + h) - f'(x))/h. Math 104: Calculus ...
In the construction of efficient numerical methods for the stiff initial value problems, some second derivative multistep methods have been introduced equipping with super future point technique. In this paper, we are going to introduce a formula for the stability functions of...
Second derivative coefficients for various grid systems are derived followingPeters' andElkins' approaches. Two simple formulae, one for three dimensional bodies and the other for two dimensional bodies are also suggested. These utilise the average of the anomalies around a single circle and the anom...
1)second derivative二阶导数 1.A class of stiffly stable k-step second derivative methods of order k+2;一类k步k+2阶的二阶导数方法 2.The infrared diffuse reflectance spectra of PP pellets and powder were directly determined, and then pretreated through multiple scattering calibration ( MSC) , ...
The advantages of the second-derivative terms were taken in order to derive numerical methods with a high order of accuracy which is stable and suitable for the numerical solution of differential equations. In particular, secondderivative of the differential system gotten from equating the problem ...
Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new WSGL formula leads to better performance compared to other known numerical ...
The theoretical orders of accuracy are equal four for the central and one-sided first derivative approximations obtained, whereas the central second derivative formula is either fourth, third, or second order accurate, depending on the grid ratio. The approximations can be used for accurate a ...
A. Konguetsof, A new two-step hybrid method for the numerical solution of the Schrödinger equation. J. Math. Chem. 47(2), 871–890 (2010) Article CAS Google Scholar F.A. Hendi, P-stable higher derivative methods with minimal phase-lag for solving second order differential equations....
2.Based on First-order Second-moment Method(FOSM),a formula for calculating t.在一次二阶矩法的基础上,推导了计算模糊随机可靠度的具体公式。 3.Reliability analysis using First Order Second Moment(FOSM)is important for structural probability design,in which process demands the derivative operation.一次...