A bstract We derive all-order expressions for perturbations of the Einstein-Hilbert action and Einstein equation with general n -th order terms. To this end, we employ Cheung Remmen’s perturbation conventions both in tensor density usual metric formalisms, including Einstein-dilaton theory. Remarkably, find minimal building blocks that generate entire each our formulations. show number terms gr...

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n−1th minors, whose solution is a representation of the nth minor as an n × n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit ...

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n−1th minors, whose solution is a representation of the nth minor as an n × n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit ...

‎second derivative general linear methods (sglms) as an extension‎ ‎of general linear methods (glms) have been introduced to improve‎ ‎the stability and accuracy properties of glms‎. ‎the coefficients of‎ ‎sglms are given by six matrices‎, ‎instead of four matrices for‎ ‎glms‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually runge--kutta stability conditions‎. ‎in this p...

This work reviews from a unified viewpoint the concepts underlying “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems” (nth-CASAM-L) and Nonlinear (nth-CASAM-N) methodologies. The practical application of nth-CASAM-L methodology is illustrated an OECD/NEA reactor physics benchmark, while nth-CASAM-N nonlinear model dynamics that...

Given scattered data on the real line, Favard [4] constructed an interpolant which depends linearly and locally on the data and whose nth derivative is locally bounded by the nth divided differences of the data times a constant depending only on n. It is shown that the (n − 1)th derivative of Favard’s interpolant can be likewise bounded by divided differences, and that one can bound at best two...

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...