Related papers: Second order differentiation formula on $RCD(K,N)$…
We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and…
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions…
We present a coordinate free approach to derive curvature formulas for pseudo-Riemannian doubly warped product manifolds in terms of curvatures of their submanifolds. We also state the geodesics equation.
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…
We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…
We consider the comparison principle for semicontinuous viscosity sub- and supersolutions of second order elliptic equations on the form $F(D^2 w,x) = 0$. A structural condition on the operator is presented that seems to unify the different…
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
In this note we give new proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via $\delta$-splitting maps. The arguments are inspired by the Cheeger-Colding theory for…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the algorithms derived by Kloeden, Platen,…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
This work presents a unified framework for the unsupervised prediction of physically plausible interpolations between two 3D articulated shapes and the automatic estimation of dense correspondence between them. Interpolation is modelled as…
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after…
In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advection-dispersion equation. The…